Bulletin of the Iranian Mathematical Society

Published by Springer Nature

Online ISSN: 1735-8515


Print ISSN: 1017-060X


Irreducible characters of Sylow p-subgroups of the Steinberg triality groups $^3D_4(p^{3m})$
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September 2013


69 Reads

In this notes we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

Topological centers of $n-$th dual of module actions

December 2010


87 Reads

In this paper, we will study the topological centers of $n-th$ dual of Banach $A-module$ and we extend some propositions from Lau and \"{U}lger into $n-th$ dual of Banach $A-modules$ where $n\geq 0$ is even number. Let $B$ be a Banach $A-bimodule$. By using some new conditions, we show that ${{Z}^\ell}_{A^{(n)}}(B^{(n)})=B^{(n)}$ and ${{Z}^\ell}_{B^{(n)}}(A^{(n)})=A^{(n)}$. We also have some conclusions in group algebras.

Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras

June 2009


57 Reads

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented. Comment: 13 pages, To appear in Bull. Iranian Math. Soc

Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras

April 2015


109 Reads

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{B}$ is prime. In this paper, we investigate the additivity of map $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies $$\Phi(AP+\eta PA^{*})=\Phi(A)\Phi(P)+\eta \Phi(P)\Phi(A)^{*},$$ for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial projection in $\mathcal{A}$. Let $\eta$ be a non-zero complex number such that $|\eta|\neq1$, then $\Phi$ is additive. Moreover, if $\eta$ is rational then $\Phi$ is $\ast$-additive.

Affinization of Segre products of partial linear spaces

April 2014


27 Reads

Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated . The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces is established. A general construction that produces non-degenerate hyperplanes in the Segre product of partial linear spaces embeddable into projective space is introduced.

Totally umbilical radical transversal lightlike hypersurfaces of K\"ahler-Norden manifolds of constant totally real sectional curvatures

July 2016


52 Reads

In this paper we study curvature properties of semi-symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,\widetilde g)$ of a K\"ahler-Norden manifold $(\overline M,\overline J,\overline g,\overline { \widetilde g})$ of constant totally real sectional curvatures $\overline \nu$ and $\overline {\widetilde \nu}$ ($g$ and $\widetilde g$ are the induced metrics on $M$ by the Norden metrics $\overline g$ and $\overline {\widetilde g}$, respectively). We obtain a condition for $\overline {\widetilde \nu}$ (resp. $\overline \nu$) which is equivalent to each of the following conditions: $(M,g)$ $(resp.\, (M,\widetilde g))$ is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.

On isomorphism of simplicial complexes and their related algebras

February 2007


133 Reads

In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as $K$-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as $K$-algebras. Based on an explicit $K$-algebra isomorphism of two Stanley-Reisner rings, or facet rings or edge rings, we present a fast algorithm to find explicitly the isomorphism of the associated simplicial complexes, or graphs.

$\sigma$-Derivations in Banach Algebras

June 2005


266 Reads

Introducing the notions of (inner) $\sigma$-derivation, (inner) $\sigma$-endomorphism and one-parameter group of $\sigma$-endomorphisms ($\sigma$-dynamics) on a Banach algebra, we correspond to each $\sigma$-dynamics a $\sigma$-derivation named as its $\sigma$-infinitesimal generator. We show that the $\sigma$-infinitesimal generator of a $\sigma$-dynamics of inner $\sigma$-endomorphisms is an inner $\sigma$-derivation and deal with the converse. We also establish a nice generalized Leibniz formula and extend the Kleinenckr--Sirokov theorem for $\sigma$-derivations under certain conditions.

Module approximate amenability of Banach algebras

January 2013


55 Reads

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying these results to $\ell^1(S)$ as an $\ell^1(E)$-module, for an inverse semigroup $S$ with the set of idempotents $E$, it is shown that $\ell^1(S)$ is module approximately amenable (contractible) if and only if it is module uniformly approximately amenable if and only if $S$ is amenable. Moreover, $\ell^1(S)^{**}$ is module (uniformly) approximately amenable if and only if a maximal group homomorphic image of $S$ is finite.

A Note on Z* algebras

July 2013


26 Reads

We study some properties of \(Z^{*}\) algebras, those \(C^{*}\) algebras whose all positive elements are zero divisors. Using an example, we show that an extension of a \(Z^{*}\) algebra by a \(Z^{*}\) algebra is not necessarily a \(Z^{*}\) algebra. However, we prove that the extension of a non-\(Z^{*}\) algebra by a non-\(Z^{*}\) algebra is a non-\(Z^{*}\) algebra. We also prove that the tensor product of a \(Z^{*}\) algebra by a \(C^{*}\) algebra is a \(Z^{*}\) algebra. As an indirect consequence of our methods, we prove the following inequality type results: (i) Let \(a_{n}\) be a sequence of positive elements of a \(C^{*}\) algebra A which converges to zero. Then, there are positive sequences \(b_{n}\) of real numbers and \(c_{n}\) of elements of A which converge to zero such that \(a_{n+k}\le b_{n}c_{k}.\) (ii) Every compact subset of the positive cones of a \(C^{*}\) algebra has an upper bound in the algebra.

Derivations into N-TH duals of ideals of banach algebras

November 2006


69 Reads

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $n\in \Bbb N$ and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\cal A},I^{(n)})=\{0\}$. Further, $\cal A$ is n-ideally amenable if $\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\cal A$. We find some relationships of $n-I-$ weak amenability and $m-J-$ weak amenability for some different m and n or for different closed ideals $I$ and $J$ of $\cal A$.

A remark on asymptotic of highest weights in tensor powers of a representation

February 2010


21 Reads

We consider the semigroup S of highest weights appearing in tensor powers V^k of a finite dimensional representation V of a connected reductive group. We describe the cone generated by S as the cone over the weight polytope of V intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in V^k in terms of the volume of this polytope.

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

June 2012


213 Reads

To demonstrate more visibly the close relation between the continuity and integrability, a new proof for the Banach-Zarecki theorem is presented on the basis of the Radon-Nikodym theorem which emphasizes on measure-type properties of the Lebesgue integral. The Banach-Zarecki theorem says that a real-valued function F is absolutely continuous on a finite closed interval if and only if it is continuous and of bounded variation when it satisfies Lusin's condition. In the present proof indeed a more general result is obtained for the Jordan decomposition of F.

An Improvement on the Base-Change Theorem and the Functor $$f^!

June 2014


43 Reads

In 2009 Lipman published his polished LNM book, the product of a decade's work, giving the definitive, state-of-the-art treatment of Grothendieck duality. In this article we achieve some sharp improvements: we begin by giving a short, sweet, new proof of the base change theorem. As it happens our proof delivers a stronger result than any of the old arguments, it allows us to handle unbounded complexes. This means that our base-change theorem must be subtle and delicate, it is right at the boundary of known counterexamples, counterexamples that had led the experts to believe that major parts of the theory could only be developed in the bounded-below derived category. Having proved our new base-change theorem, we then use it to define the functor $f^!$ on the unbounded derived category and establish its functoriality properties. In Section 1 we will use this to clarify the relation among all the various constructions of Grothendieck duality. One illustration of the power of the new methods is that we can improve Lipman's Theorem 4.9.4 to handle complexes that are not necessarily bounded. We also present applications to the theory developed by Avramov, Iyengar, Lipman and Nayak on the connection between Grothendieck duality and Hochschild homology and cohomology.

Properties of Generalized Berwald Connections

March 2009


82 Reads

Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here the properties of one of these classes namely the Berwald-type connections which contains Berwald and Chern(Rund) connections as a special case is studied. It is proved among the other that the hv-curvature of these connections vanishes if and only if the Finsler space is a Berwald one. Some applications of this connection is discussed.

Binomial edge ideals and rational normal scrolls

October 2015


123 Reads

Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is given.

Upper and Lower Bounds for Numerical Radii of Block Shifts

October 2014


25 Reads

For any $n$-by-$n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & & \\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we consider two $k$-by-$k$ matrices \[A'=[\begin{array}{cccc} 0 & \|A_1\| & & \\ & 0 & \ddots & \\ & & \ddots & \|A_{k-1}\| \\ & & & 0\end{array}] \ {and} \ A''=[\begin{array}{cccc} 0 & m(A_1) & & \\ & 0 & \ddots & \\ & & \ddots & m(A_{k-1}) \\ & & & 0\end{array}],\] where $\|\cdot\|$ and $m(\cdot)$ denote the operator norm and minimum modulus of a matrix, respectively. It is shown that the numerical radii $w(\cdot)$ of $A$, $A'$ and $A''$ are related by the inequalities $w(A'')\le w(A)\le w(A')$. We also determine exactly when either of the inequalities becomes an equality.

On a Conjecture of a Bound for the Exponent of the Schur Multiplier of a Finite $p$-Group

November 2010


28 Reads

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp(G)$ and let $m=\lfloor\log_pk\rfloor$. We show that $\exp(M^{(c)}(G))$ divides $\exp(G)p^{m(k-1)}$, for all $c\geq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $\exp(M(G))$ divides $\exp(G)$ for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement of some previous bounds for the exponent of $M^{(c)}(G)$ given by M. R. Jones, G. Ellis and P. Moravec in some cases. Comment: 8 pages, to appear in Bulletin of the Iranian Mathematical Society

k-forested choosability of graphs with bounded maximum average degree

February 2011


42 Reads

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prove that the $k$-forested choosability of a graph with maximum degree $\Delta\geq k\geq 4$ is at most $\lceil\frac{\Delta}{k-1}\rceil+1$, $\lceil\frac{\Delta}{k-1}\rceil+2$ or $\lceil\frac{\Delta}{k-1}\rceil+3$ if its maximum average degree is less than 12/5, $8/3 or 3, respectively.

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