Article

Hermitian forms on algebras over local rings

January 1994

Authors:

Laura Fainsilber

Chalmers University of Technology

Clifford theory of Weil representations of unitary groups

Article

Jun 2019

Let {\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of {\mathcal{O}} by a nonzero power of its maximal ideal, and let {*} be the involution that A inherits from {\mathcal{O}} . We consider various unitary groups {\mathcal{U}_{m}(A)} of rank m over A , depending on the nature of {*} and the equivalence type of the underlying hermitian or skew hermitian form. Each group {\mathcal{U}_{m}(A)} gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the Weil representation of {\mathcal{U}_{m}(A)} with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.

ResearchGate has not been able to resolve any references for this publication.

Article

Full-text available

Comparison of topologies on aZ-algebras of locally measurable operators

January 2010 · Positivity

We consider the locally measure topology

t(\mathcal{M})

on the *-algebra

LS(\mathcal{M})

of all locally measurable operators affiliated with a von Neumann algebra

\mathcal{M}

. We prove that

t(\mathcal{M})

coincides with the (o)-topology on

LS_h(\mathcal{M})=\{T\in LS(\mathcal{M}): T^*=T\}

if and only if the algebra

\mathcal{M}

is

\sigma

-finite and a finite algebra. We study ... [Show full abstract] relationships between the topology

t(\mathcal{M})

and various topologies generated by faithful normal semifinite traces on

\mathcal{M}

. Comment: 21 pages

Article

Examples of non-commutative crepant resolutions of Cohen Macaulay normal domains

June 2014 · Journal of Algebra

Tony J. Puthenpurakal

Let A be a Cohen-Macaulay normal domain. A non commutative crepant resolution (NCCR) of A is an A-algebra

\Gamma

of the form

\Gamma = End_A(M)

, where M is a reflexive A-module,

\Gamma

is maximal Cohen-Macaulay as an A-module and

gldim(\Gamma)_P = \dim A_P

for all primes P of A. We give bountiful examples of equi-characteristic Cohen-Macaulay normal local domains and mixed ... [Show full abstract] characteristic Cohen-Macaulay normal local domains having NCCR. We also give plentiful examples of affine Cohen-Macaulay normal domains having NCCR.

Article

Non-normal affine monoids

September 2012

Lukas Katthän

We give a geometric description of the set of holes in a non-normal affine monoid Q. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of k[Q]. From this, we see how various properties of k[Q] like local normality and Serre's conditions

(R_1)

and

(S_2)

are encoded in the geometry of the holes. A combinatorial upper bound for the depth ... [Show full abstract] the monoid algebra k[Q] is obtained and some cases where equality holds are identified. We apply this results to seminormal affine monoids.

Article

Full-text available

Desingularization preserving stable simple normal crossings

November 2013 · Israel Journal of Mathematics

The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X,D), where D is a divisor on X), we construct a functorial desingularization of all but stable simple normal crossings (stable-snc) singularities, by smooth blowings-up that preserve such singularities. A variety has stable simple ... [Show full abstract] normal crossings at a point if, locally, its irreducible components are smooth and tranverse in some smooth embedding variety. We also show that our main assertion is false for more general simple normal crossings singularities.

Article

Locally finite weights on von Neumann algebras, and quadratic forms

January 1985

N.V. Trunov

Article

Full-text available

Specialization of Rees algebras with a view to tangent star algebras

January 1970

One shows that if S is a noetherian ring and J⊂S is an ideal such that the associated graded ring gr J (S) is Cohen-Macaulay then the Rees algebra ℛ(J) specializes if and only if the local analytic spreads of J are conveniently bounded above. Moreover, if this is the case, then the specialized associated graded ring is Cohen-Macaulay. This partly improves a previous result of Eisenbud-Huneke. ... [Show full abstract] Applications are given to the theory of tangent star algebras yielding further insight into the well-known one-parameter deformations of the cone on the rational normal quartic.

Article

Local invariants and exceptional divisors of group actions

January 2016 · Journal of Algebra

Lex E. Renner

We consider linear algebraic groups and algebraic varieties defined over the field k. We always assume that k is algebraically closed. Starting with an action G×. X→. X, on the normal, quasi-affine variety X, we analyse the maximal G-finite subalgebra OK of k(X). We also analyse the maximal G-finite subalgebra OK(p) of k[X]p, where p is a height-one G-invariant prime ideal of k[. X]. We use our ... [Show full abstract] findings to assess the behaviour of the canonical map π:U→U//G≡Spec(O(U)G) for a G-invariant, open subset U of X. It turns out that for any G-invariant divisor D, there is a G-invariant, open subset V such that V∩. D≠. θ and the canonical morphism π :. V→. V//. G has no exceptional divisors.

Article

Full-text available

Normal Ideals In Regular Rings

October 1998 · Journal für die reine und angewandte Mathematik

We study the Cohen-Macaulay property of the Rees algebra of a normal ideal of a regular local ring. In particular we characterize this property in the 3-dimensional case, assuming the ideal is 4-generated, has height 2, is unmixed, and is generically a complete intersection. Our characterization yields concrete examples of normal ideals whose Rees algebras are not Cohen-Macaulay, thus settling a ... [Show full abstract] recent conjecture of Vasconcelos. We also provide a two-dimensional algebraic proof of a version (due to Sancho de Salas) of a vanishing theorem proved by Grauert and Riemenschneider, plus an explicit example illustrating that the version fails in dimension 3. This example complements a family of such examples constructed geometrically by Cutkosky.

Article

Normal Ideals and Expected Reduction Numbers #

September 2005 · Communications in Algebra

We give a criterion for normality of certain strongly Cohen-Macaulay ideals, of a regular local ring, having the expected reduction number.

Article

Local uniform approximation by functions in a uniform algebra

June 1983 · Rocky Mountain Journal of Mathematics

David M. Wells

Article

Full-text available

Rees algebras and $p_g$ -ideals in a two-dimensional normal local domain

November 2015 · Proceedings of the American Mathematical Society

The authors introduced the notion of

p_g

-ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In this note, we give several ring-theoretic characterization of

p_g

-ideals. For instance, an m-primary ideal

I \subset A

is a

p_g

-ideal if and only if the Rees alegbra

\mathcal{R}(I)

is a Cohen-Macaulay normal ... [Show full abstract] domain.

Article

Estimates and sheaves. On some questions of nonstandard analysis

January 1970

V.A. Lyubetskij