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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 ...
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis
Derivations and Projections Jordan Triples nonassociative algebra continuous cohomology quantum functional analysis Operator Algebras
2012/6/19
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
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...
Thoughts on Eggert's Conjecture
Eggert’s Conjecture Frobenius map on a finite-dimensional nilpotent commutative algebra finite abelian semigroup
2012/6/15
Eggert's Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R^{(p)} is the image of the p-th power map on R, then dim_F R \...
On the Chern number of $I$-admissible filtrations of ideals
Chern number $I$-admissible filtrations of ideals Commutative Algebra
2012/5/24
Let $I$ be an $\m$-primary ideal of a Noetherian local ring $(R, \m)$ of positive dimension. The coefficient $e_1(\mathcal I)$ of the Hilbert polynomial of an $I$-admissible filtration $\mathcal I$ is...
Minimal primes of ideals arising from conditional independence statements
conditional independence statements Commutative Algebra
2011/9/22
Abstract: We consider ideals, arising in the context of conditional independence models, that generalize those considered by Fink [6] in a way distinct from the generalization of [11]. We describe the...
Lyubeznik numbers of monomial ideals
Lyubeznik numbers monomial ideals Commutative Algebra
2011/9/21
Abstract: We study Bass numbers of local cohomology modules supported on squarefree monomial ideals paying special attention to Lyubeznik numbers. We build a dictionary between local cohomology module...
Lower bounds for finiteness of generalized local cohomology modules and their associated primes
Generalized local cohomology modules associatted prime Serre subcategories
2011/9/20
Abstract: Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. In this paper, we study relations between f...
Cohen-Macaulayness of generically complete intersection monomial ideals
Cohen-Macaulay generically complete intersection monomial ideals Commutative Algebra
2011/9/20
Abstract: In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete...
Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
symbolic powers multigraded points
2011/9/20
Abstract: Let I be a homogeneous ideal of R = k[x_0,...,x_n]. A current research theme is to compare the symbolic powers of I with the regular powers of I. In this paper, we investigate which ordinary...
Factoring formal power series over principal ideal domains
power series principal ideal domains Commutative Algebra
2011/9/20
Abstract: We provide an irreducibility test and factoring algorithm (with some qualificiations) for formal power series in the unique factorization domain $R[[X]]$, where $R$ is any principal ideal do...
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 ...
Representations of finite groups: Local cohomology and support
Representations of finite groups Local cohomology Commutative Algebra
2011/9/20
Abstract: These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010.
Decompositions of commutative monoid congruences and binomial ideals
Decompositions of commutative monoid congruences binomial ideals Commutative Algebra
2011/9/19
Abstract: We demonstrate how primary decomposition of commutative monoid congruences fails to capture the essence of primary decomposition in commutative rings by exhibiting a more sensitive theory of...
On the Koszul property of toric face rings
Koszul property toric face rings Commutative Algebra
2011/9/19
Abstract: Toric face rings is a generalization of the concepts of affine semigroup rings and Stanley-Reisner rings. We characterize toric face rings having the Koszul, strongly Koszul or initially Kos...