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Ternary Weakly Amenable C*-algebras and JB*-triples     C*-algebras and JB*-triples  Operator Algebras       font style='font-size:12px;'> 2012/6/19
A well known result of Haagerup from 1983 states that every C*-algebra A is weakly amenable, that is, every (associative) derivation from A into its dual is inner. A Banach algebra B is said to be ter...
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from...
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the bi...
Poincare duality for Koszul algebras     Poincare duality  Koszul algebras  Quantum Algebra       font style='font-size:12px;'> 2012/5/24
We discuss the consequences of the Poincar\'e duality, versus AS- Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincar\'e duality pr...
It is shown that in every multiplicative right Hom-alternative algebra, a Hom-type generalization of the Mikheev identity holds. It is then inferred that a multiplicative right Hom-alternative algebra...
We show that a $C^\star$-algebra $B$ contains a dense Fr\'echet two-sided ideal $A$ satisfying seminorm inequalities $\| a_1 a_2 \|_n \leq \min \bigl\{\, \|a_1\|_n \|a_2\|_B,\, \|a_1\|_B \|a_2\|_n \...
We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is ex...
A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field...
We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter-Drinfeld resolution of the counit of $A$ to the sam...
The aim of our paper is twofold. First, we thoroughly study the set of meager elements $M(E)$, the set of sharp elements $S(E)$ and the center $C(E)$ in the setting of meager-orthocomplete homogeneous...
The aim of our paper is to prove the Triple Representation Theorem, which was established by Jen\v{c}a in the setting of complete lattice effect algebras, for a special class of homogeneous effect alg...
Free evolution on algebras with two states II     Free evolution  algebras  two states II  Operator Algebras       font style='font-size:12px;'> 2012/4/17
Denote by $J$ the operator of coefficient stripping. We show that for any free convolution semigroup of measures $\nu_t$ with finite variance, applying a single stripping produces semicircular evoluti...
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a comp...
Asymptotic Hecke algebras and involutions     Asymptotic Hecke algebras  involutions  Representation Theory       font style='font-size:12px;'> 2012/4/17
In a previous paper the author and D. Vogan defined and studied a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group. In this paper this study is continued by ...
We prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing...

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