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We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as ...
Ternary Weakly Amenable C*-algebras and JB*-triples
C*-algebras and JB*-triples Operator Algebras
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...
Sperner property and finite-dimensional Gorenstein algebras associated to matroids
Sperner property finite-dimensional Gorenstein algebras matroids Commutative Algebra
2011/9/21
Abstract: We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. We ...
Artinian level algebras of codimension 3
Hilbert functions Level O-sequences Artinian Level algebras Reduction numbers Generic initial ideals Graded Betti numbers
2011/9/15
Abstract: In this paper, we continue the study of which $h$-vectors $\H=(1,3,..., h_{d-1}, h_d, h_{d+1})$ can be the Hilbert function of a level algebra by investigating Artinian level algebras of cod...
C*-algebras nearly contained in type I algebras
C*-algebras Near inclusions Perturbations Type I C*-algebras Similarity Problem
2011/9/1
Abstract: In this paper we consider near inclusions $A\subseteq_\gamma B$ of C$^*$-algebras. We show that if $B$ is a separable type I C*-algebra and $A$ satisfies Kadison's similarity problem, then $...
Abstract: Using the method of commutative algebra, we show that the set $\mathfrak{R}$ of nilpotent elements of a vertex algebra $V$ forms an ideal, and $V/\mathfrak{R}$ has no nonzero nilpotent eleme...
On stably free modules over affine algebras
stably free modules affine algebras Grothendieck-Witt groups symplectic Witt groups
2011/8/25
Abstract: We prove that stably free modules of rank d-1 over a smooth affine algebra of dimension d over an algebraically closed field k are free, provided (d-1)! is nonzero in k.
Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra
Gr¨obner-Shirshov basis non-associative algebra commutative algebra
2010/11/26
We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative algebra over an arbi...