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Ternary Weakly Amenable C*-algebras and JB*-triples
C*-algebras and JB*-triples Operator Algebras
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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...
Towards applications of graded Paraparticle algebras
Relative Paraparticle algebras general linear superalgebra multiple-level system
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2012/6/19
An outline is sketched, of applications of the ideas and the mathematical methods presented at the 19th symposium of the Hellenic Nuclear Physics Society (HNPS) in Thessaloniki, May 2010.
Rigidification of algebras over essentially algebraic theories
homotopy limit theory homotopy model rigidification
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2012/6/18
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...
Augmented down-up algebras and uniform posets
Uniform poset dual polar space dual polar graph down-up algebra
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2012/6/19
Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related to the down-up algebras defined by Benkart an...
On the algebraic K-theory of truncated polynomial algebras in several variables
algebraic K-theory truncated polynomial algebras several variables Algebraic Topology
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2012/6/14
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
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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...
The Mikheev identity in right Hom-alternative algebras
Right Hom-alternative algebra Mikheev identity Rings and Algebras
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2012/5/9
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...
Dense nuclear Frechet ideals in $C^\star$-algebras
Dense nuclear Frechet ideals Operator Algebras Functional Analysis
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2012/5/9
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 \...
A characterization of amenability of group actions on $C^\ast$-algebras
characterization amenability group actions $C^\ast$-algebras
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2012/4/16
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...
Twisted split category algebras as quasi-hereditary algebras
Group Theory category algebras quasi-hereditary algebras
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2012/4/16
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...
Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit
Hochschild homology of Hopf algebras free Yetter-Drinfeld resolutions the counit K-Theory and Homology
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2012/4/18
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...
Triple Representation Theorem for orthocomplete homogeneous effect algebras
homogeneous effect algebra orthocomplete effect algebra meager-orthocomplete effect algebra lattice effect algebra center
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2012/4/18
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...
Triple Representation Theorem for homogeneous effect algebras
Homogeneous effect algebra TRT-effect algebra orthocomplete effect algebra lattice effect algebra
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2012/4/18
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
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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...
Reflexive Operator Algebras on Banach Spaces
operator algebras invariant subspace lattice Boolean algebra of projections spectral operator
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2012/4/18
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...