Dana P. Williams

• PhD
• Professor (Full) at Dartmouth College

Well-known work of Renault shows that if $\mathcal{E}$ is a twist over a second countable, effective, étale groupoid $G$, then there is a naturally associated Cartan subalgebra of the reduced twisted groupoid $C^{*}$-algebra $C^{*}_{r}(G;\mathcal{E})$, and that every Cartan subalgebra of a separable $C^{*}$-algebra arises in this way. However, twis...

We use the Ladder Technique to establish bijections between the ideals of related Fell bundles.

We present a new method of establishing a bijective correspondence - in fact, a lattice isomorphism - between action- and coaction-invariant ideals of C*-algebras and their crossed products by a fixed locally compact group. It is known that such a correspondence exists whenever the group is amenable; our results hold for any locally compact group u...

We establish a generalized Rieffel correspondence for ideals in equivalent Fell bundles.

If p:B→G is a Fell bundle over an étale groupoid, then we show that there is an norm reducing injective linear map j:Cr⁎(G;B)→Γ0(G;B) generalizing the well know map j:Cr⁎(G)→C0(G) in the case of an étale groupoid.

We show that groupoid equivalence preserves a number of groupoid properties such as properness or the property of being topologically principal.

We analyse extensions $\Sigma$ of groupoids G by bundles A of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid G by a given bundle A. There is a natural action of Sigma on the dual of A, yielding a corresponding transformation groupoid. The pushout of this transfo...

We study the topology of the primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelain stabilizers. Furthermore, we obtain complete results when the isotropy map is continuous except for jump discontinuities, and also when $G$ is a unit space fixing ext...

We analyse extensions $\Sigma$ of groupoids $G$ by bundles $A$ of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid $G$ by a given bundle $A$. There is a natural action of $\Sigma$ on the dual of $A$, yielding a corresponding transformation groupoid. The pushout of...

Given an action of a groupoid by isomorphisms on a Fell bundle (over another groupoid), we form a semidirect-product Fell bundle, and prove that its $C^{*}$-algebra is isomorphic to a crossed product.

Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essent...

Given a normal subgroup bundle A of the isotropy bundle of a groupoid Σ, we obtain a twisted action of the quotient groupoid Σ/A on the bundle of group C⁎-algebras determined by A whose twisted crossed product recovers the groupoid C⁎-algebra C⁎(Σ). Restricting to the case where A is abelian, we describe C⁎(Σ) as the C⁎-algebra associated to a T-gr...

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algbras determined by $\mathcal A$ whose twisted crossed product recovers the groupoid $C^*$-algebra $C^*(\Sigma)$. Restricting to the case where $\mathcal A$...

Given a locally compact abelian group $G$, we give an explicit formula for the Dixmier--Douady invariant of the $C^*$-algebra of the groupoid extension associated to a \v{C}ech $2$-cocycle in the sheaf of germs of continuous $G$-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central exte...

Given a locally compact abelian group $G$, we give an explicit formula for the Dixmier--Douady invariant of the $C^*$-algebra of the groupoid extension associated to a \v{C}ech $2$-cocycle in the sheaf of germs of continuous $G$-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central exte...

The reduced C*-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid G embeds as a C*-subalgebra of the reduced C*-algebra of G. We prove that any representation of the reduced algebra of G that is injective on this subalgebra is faithful. We also show that restriction of functions extends to a faithful conditional expectation o...

We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C ∗-algebra. For a special class of actions we describe the Jacobson topology.

We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full a...

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful....

For second countable locally compact Hausdorff groupoids, the property of possessing a Haar system is preserved by equivalence.

We consider the amenability of of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$. We show that our result is...

We show that if $(A,G,\alpha)$ is a groupoid dynamical system with $A$ continuous trace, then the crossed product $A\rtimes_{\alpha}G$ is Morita equivalent to the C*-algebra $C*(\uG,\uE)$ of a twist $\uE$ over a groupoid $\uG$ equivalent to $G$. This is a groupoid analogue of the well know result for the crossed product of a group acting on an elem...

In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel surjection of the first paper in the series to relate our version of Mansfield’s theorem to that of Huef and Raeburn, and to give an automatic amenability result for...

We give precise conditions under which irreducible representations associated to stability groups induce to irreducible representations for Fell bundle C*-algebras. This result generalizes an earlier result of Echterhoff and the second author. Because the Fell bundle construction subsumes most other examples of C*-algebras constructed from dynamica...

We examine the ideal structure of crossed products B\rtimes G where B is a continuous-trace C*-algebra and the induced action of G on the spectrum of B is proper. In particular, we are able to obtain a concrete description of the topology on the spectrum of the crossed product in the cases where either G is discrete or G is a Lie group acting smoot...

In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel Surjection of the first paper in the series to relate our version of Mansfield's theorem to that of an Huef and Raeburn, and to give an automatic amenability result...

We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several ap...

Given groupoids $G$ and $H$ and a $(G,H)$-equivalence $X$ we may form the transformation groupoid $G\ltimes X\rtimes H$. Given a separable groupoid dynamical system $(A,G\ltimes X\rtimes H,\omega)$ we may restrict $\omega$ to an action of $G\ltimes X$ on $A$ and form the crossed product $A\rtimes G\ltimes X$. We show that there is an action of $H$...

Our goal in this paper and two sequels is to apply the Yamagami-Muhly-Williams equivalence theorem for Fell bundles over groupoids to recover and extend all known imprimitivity theorems involving groups. Here we extend Raeburn's symmetric imprimitivity theorem, and also, in an appendix, we develop a number of tools for the theory of Fell bundles th...

We establish conditions under which the universal and reduced norms coincide for a Fell bundle over a groupoid. Specifically, we prove that the full and reduced C*-algebras of any Fell bundle over a measurewise amenable groupoid coincide, and also that for a groupoid G whose orbit space is T_0, the full and reduced algebras of a Fell bundle over G...

We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced C*-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid C*-algebras. Comment: 14 Pages, added references with minor changes to the introduction and the end of section one

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results genera...

Suppose that a locally compact group G acts freely and properly on the right of a locally compact space T. Rieffel proved that if α is an action of G on a C *-algebra A and there is an equivariant embedding of C 0(T) in M(A), then the action α of G on A is proper, and the crossed product \(A\rtimes_{\alpha,r}G\) is Morita equivalent to a generalise...

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a subgroup. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent, and hence have the same representation theory. Here we consider commuting actions of...

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we use definitions and constructions that are well-documented and accessible to non-experts, and otherwise we pr...

We show that if $p:\B\to G$ is a Fell bundle over a locally compact groupoid $G$ and that $A=\Gamma_{0}(G^{(0)};\B)$ is the \cs-algebra sitting over $G^{(0)}$, then there is a continuous $G$-action on $\Prim A$ that reduces to the usual action when $\B$ comes from a dynamical system. As an application, we show that if $I$ is a $G$-invariant ideal i...

We show how to extend a classic Morita Equivalence Result of Green's to the \cs-algebras of Fell bundles over transitive groupoids. Specifically, we show that if $p:\B\to G$ is a saturated Fell bundle over a transitive groupoid $G$ with stability group $H=G(u)$ at $u\in \go$, then $\cs(G,\B)$ is Morita equivalent to $\cs(H,\CC)$, where $\CC=\B\rest...

We show that if $\AA$ is a Fell bundle over a locally compact group $G$, then there is a natural coaction $\delta$ of $G$ on the Fell-bundle $C^*$-algebra $C^*(G,\AA)$ such that if $\hat{\delta}$ is the dual action of $G$ on the crossed product $C^*(G,\AA) \rtimes_{\delta} G$, then the full crossed product $(C^*(G,\AA) \rtimes_{\delta}G)\rtimes_{\h...

We consider two categories of C*-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C*-algebraic contexts. We show that Rieffel's construction of a fixed-point alg...

We consider a fixed free and proper action of a locally compact group $G$ on a space $T$, and actions $\alpha:G\to \Aut A$ on $C^*$-algebras for which there is an equivariant embedding of $(C_0(T),\rt)$ in $(M(A),\alpha)$. A recent theorem of Rieffel implies that $\alpha$ is proper and saturated with respect to the subalgebra $C_0(T)AC_0(T)$ of $A$...

We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. We then provide a necessary and...

The generalized Effros-Hahn conjecture for groupoid C*-algebras says that, if G is amenable, then every primitive ideal of the groupoid C*-algebra C*(G) is induced from a stability group. We prove that the conjecture is valid for all second countable amenable locally compact Hausdorff groupoids. Our results are a sharpening of previous work of Jean...

We study the C*-algebras of Fell bundles. In particular, we prove the analogue of Renault's disintegration theorem for groupoids. As in the groupoid case, this result is the key step in proving a deep equivalence theorem for the C*-algebras of Fell bundles.

If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

We discuss some results and open questions related to the Mackey machine for C * -crossed products. The celebrated Gootman–Rosenberg–Sauvageot proof of the validity of the generalized Effros–Hahn conjecture shows that all primitive ideals of a separable crossed product are induced in an appropriate sense from a stability group. Here we address the...

If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

Let δ be a maximal coaction of a locally compact group G on a C*-algebra B, and let N and H be closed normal subgroups of G with N ⊆ H. We show that the process IndG / HG which uses Mansfield's bimodule to induce representations of B ⋊δ G from those of B ⋊δ | (G / H) is equivalent to the two-stage induction process IndG / NG ○ IndG / HG / N. The pr...

We provide an exposition and proof of Renault's equivalence theorem for crossed products by locally Hausdorff, locally compact groupoids. Our approach stresses the bundle approach, concrete imprimitivity bimodules and is a preamble to a detailed treatment of the Brauer semigroup for a locally Hausdorff, locally compact groupoid.

We show that important structural properties of C*-algebras and the multiplicity numbers of representations are preserved under Morita equivalence.

The classical Chase–Harrison–Rosenberg exact sequence relates the Picard and Brauer groups of a Ga-lois extension S of a commutative ring R to the group cohomology of the Galois group. We associate to each action of a locally compact group G on a locally compact space X two groups which we call the equivariant Picard group and the equivariant Braue...

Let B be a C*-algebra with a maximal coaction of a locally compact group G, and let N and H be closed normal subgroups of G with N contained in H. We show that the process Ind_(G/H)^G which uses Mansfield's bimodule to induce representations of the crossed product of B by G from those of the restricted crossed product of B by (G/H) is equivalent to...

We study conditions on a C * -dynamical system (A,G,α) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A⋊ α G. The results build on earlier results of Sauvageot and...

We prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups H and K on a C*-algebra.

We consider the following problem. Suppose $\alpha$ is an action of a locally compact group $G$ on a $C^*$-algebra $A$, $H$ is a closed subgroup of $G$, and $(\pi,U)$ is a covariant representation of $(A,H,\alpha)$. For which closed subgroups $K$ containing $H$ is there a covariant representation $(\pi,V)$ of $(A,K,\alpha)$ such that $V|_H=U$? We a...

We give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

Let G G be a second countable, locally compact groupoid with Haar system, and let A \mathcal {A} be a bundle of C ∗ C^{\ast } -algebras defined over the unit space of G G on which G G acts continuously. We determine conditions under which the associated crossed product C ∗ ( G ; A ) C^{\ast }(G;\mathcal {A}) is a continuous trace C ∗ C^{\ast } -alg...

We study that natural inclusions $C^b(X) \tensor A$ into $C^b(X,A)$ and $C^b(X, C^b(Y))$ into $C^b(X \times Y)$. In particular, excepting trivial cases, both these maps are isomorphisms only when $X$ and $Y$ are pseudocompact. This implies a result of Glicksberg showing that the Stone-Cech compactificiation $\beta(X \times Y)$ is naturally identifi...

We give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary $C^*$-algebras that satisfies Fell's condition.

Let $G$ be a second countable, locally compact groupoid with Haar system, and let $\mathcal{A}$ be a bundle of $C^{\ast}$-algebras defined over the unit space of $G$ on which $G$ acts continuously. We determine conditions under which the associated crossed product $C^{\ast}(G;\mathcal{A})$ is a continuous trace $C^{\ast}$-algebra.

We examine the structure of central twisted transformation group C ∗-algebras C0(X) ⋊id,u G, and apply our results to the group C ∗-algebras of central group extensions. Our methods require that we study Moore’s cohomology group H 2 ( G, C(X,T) ) , and, in particular, we prove an inflation result for pointwise trivial cocyles which may be of use el...

We initiate a careful study of a generalized symmetric imprimitivity theory for commuting proper actions of locally compact groups H and K on a C*-algebra.

We characterize the ideal of continuous-trace elements in a Separable transformation-group C*-algebra C-0(X) x G. In addition, we identify the largest Fell ideal, the largest liminal ideal and the largest postliminal ideal.

We consider a class of proper actions of locally compact groups on imprimitivity bimodules over C∗-algebras which behave like the proper actions on C∗-algebras introduced by Rieffel in 1988. We prove that every such action gives rise to a Morita equivalence between a crossed product and a generalized fixed-point algebra, and in doing so make severa...

We consider a class of proper actions of locally compact groups on imprimitivity bimodules over C*-algebras which behave like the proper actions on C*-algebras introduced by Rieffel in 1988. We prove that every such action gives rise to a Morita equivalence between a crossed product and a generalized fixed-point algebra, and in doing so make severa...

We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors W_E : G^0 -> N which describe how the sinks are attached to G; more precisely, the...

We make a detailed study of locally inner actions on C *-algebras whose primitive ideal spaces have locally compact Hausdorff complete regularizations. We suppose that G has a representation group and compactly generated abelianization Gab. Then, if A is stable and if the complete regularization of Prim(A) is X, we show that the collection of exter...

. Suppose that (X, G) is a second countable locally compact transformation group. We let SG (X) denote the set of Morita equivalence classes of separable dynamical systems (A, G, #)whereA is a C0 (X)-algebra and # is compatible with the given G-action on X.WeprovethatS G (X)isa commutative semigroup with identity with respect to the binary operatio...

. We characterize the ideal of continuous-trace elements in a separable transformation-group C -algebra C0 (X) oG. In addition, we identify the largest Fell ideal, the largest liminal ideal and the largest postliminal ideal. 1. Introduction Let (G; X) be a locally compact Hausdorff transformation group: thus G is a locally compact Hausdorff group a...

Suppose that ( X , G ) (X,G) is a second countable locally compact transformation group. We let S G ⁡ ( X ) \operatorname {S}_G(X) denote the set of Morita equivalence classes of separable dynamical systems ( A , G , α ) (A,G,\alpha ) where A A is a C 0 ( X ) C_{0}(X) -algebra and α \alpha is compatible with the given G G -action on X X . We prove...

This article is intended to answer the question “Why do you guys always want to twist everything?” We review the various ways in which twists, twisted actions and twisted crossed products arise, and then discuss some cohomological obstructions to the existence and triviality of twisted actions.

. Suppose that (G; T ) is a second countable locally compact transformation group given by a homomorphism ` : G ! Homeo(T ), and that A is a separable continuous-trace C -algebra with spectrum T . An action ff : G ! Aut(A) is said to cover ` if the induced action of G on T coincides with the original one. We prove that the set Br G (T ) of Morita e...

Suppose thatGhas a representation groupH, thatGab≔G/ is compactly generated, and thatAis aC*-algebra for which the complete regularization of Prim(A) is a locally compact Hausdorff spaceX. In a previous article, we showed that there is a bijectionα↦(Zα, fα) between the collection of exterior equivalence classes of locally inner actionsα: G→Aut(A),...

We make a detailed study of locally inner actions on C*-algebras whose primitive ideal spaces have locally compact Hausdorff complete regularizations. We suppose that $G$ has a representation group and compactly generated abelianization $G_{ab}$. Then if the complete regularization of $\Prim(A)$ is $X$, we show that the collection of exterior equiv...

Suppose that $G$ has a representation group $H$, that $G_{ab}:= G/\bar{[G,G]}$ is compactly generated, and that $A$ is a \cs-algebra for which the complete regularization of $\Prim(A)$ is a locally compact Hausdorff space $X$. In a previous article, we showed that there is a bijection $\alpha \mapsto (Z_\alpha,f_\alpha)$ between the collection of e...

We define the Brauer group $\Br(G)$ of a locally compact groupoid $G$ to be the set of Morita equivalence classes of pairs $(\A,\alpha)$ consisting of an elementary C*-bundle $\A$ over $G^{(0)}$ satisfying Fell's condition and an action $\alpha$ of $G$ on $\A$ by $*$-isomorphisms. When $G$ is the transformation groupoid $X\times H$, then $\Br(G)$ i...

Suppose that (G, T) is a second countable locally compact transformation group given by a homomorphism ℓ: G→Homeo(T), and thatAis a separable continuous-traceC*-algebra with spectrumT. An actionα: G→Aut(A) is said to cover ℓ if the induced action ofGonTcoincides with the original one. We prove that the set BrG(T) of Morita equivalence classes of su...

Suppose that G is a second countable locally compact groupoid with a Haar system and with abelian isotropy. We show that the groupoid C * -algebra C * (G, λ) has continuous trace if and only if there is a Haar system for the isotropy groupoid A and the action of the quotient groupoid G/A is proper on the unit space of G.

We characterize when the primitive ideal space of a crossed product $\acg$ of a \cs-algebra $A$ by a locally compact abelian group $G$ is a $\sigma$-trivial $\ghat G$-space for the dual $\ghat G$-action. Specifically, we show that $\Prim(\acg)$ is $\sigma$-trivial if and only if the quasi-orbit space is Hausdorff, the map which assigns to each quas...

We characterize when the primitive ideal space of a crossed product $\acg$ of a \cs-algebra $A$ by a locally compact abelian group $G$ is a $\sigma$-trivial $\ghat G$-space for the dual $\ghat G$-action. Specifically, we show that $\Prim(\acg)$ is $\sigma$-trivial if and only if the quasi-orbit space is Hausdorff, the map which assigns to each quas...

If $X$ is a locally compact space which admits commuting free and proper actions of locally compact groups $G$ and $H$, then the Brauer groups $\Br_H(G/X)$ and $\Br_G(X/H)$ are naturally isomorphic.

Continuous-trace C *-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C 0 ( T ). The Dixmier-Douady class δ( A ) is an element of the Čech cohomology group Ȟ ³ ( T , ℤ) and is the obstruction to building a global equivalence from the local equivalences. Here we shall be concerned with systems (...

A separable C*-dynamical system (A, G, α) in which A is a continuous-trace C*-algebra and G is Abelian is called N-principal if N is a closed subgroup of G such that α restricted to N is locally unitary and the action of G on  defines a principal bundle p(α):  → A/G. In this event, it is known that the spectrum of A ×|αG is a principal N̂-bundle...

Absract Let ξ be a C *;-bundle over T with fibres { A t } t∈ A . Suppose that A is the C *-algebra of sections of ξ which vanish at infinity, and that ( A , G , α) is a C *-dymanical system that, for each t ∈ T , the ideal I t = { f ∈ A | f ( t ) =; 0} is G -invariant. If in addition, the stabiliser group of each P ∈ Prim( A ) is amenable, then A ⋊...

An equivariant completely bounded linear operator between two C*-algebras acted on by an amenable group is shown to lift to a completely bounded operator between the crossed products that is equivariant with respect to the dual coactions. A similar result is proved for coactions and dual actions. It is shown that the only equivariant linear operato...

Let (A, G, α) be a C∗-dynamical system with G abelian and  Hausdorff. We investigate the ideal structure of the crossed product A × G under the hypothesis that the stabiliser subgroups for the action of G on  vary continuously. We discuss a new notion of locally trivial G-space for such actions, and, dually, actions α which are locally unitarily...

Let G be a locally compact group and p: Ω → T a principal G-bundle. If A is a C*-algebra with primitive ideal space T, the pull-back p* A of A along p is the balanced tensor product C0(Ω) ⊗C(T) A. If $\beta: G \rightarrow \operatorname{Aut} A$ consists of C(T)-module automorphisms, and $\gamma: G \rightarrow \operatorname{Aut} C_0(\Omega)$ is the n...

Suppose that a locally compact group G acts on strongly Monta equivalent C*-algebras A and B and let A ⋊ G and B ⋊ G denote the corresponding crossed products. We present conditions which imply that A ⋊ G and B ⋊ G are also strongly Monta equivalent and we apply our result to improve upon known theorems concerning strong Morita equivalence between...