Derived equivalence classification of Brauer graph algebras

Derived Equivalence Classification of Symmetric Algebras of Polynomial Growth

We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to derived equivalence. Introduction and the main result Throughout the article, K will denote a fixed algebraically closed field. By an algebra is meant an associati...

The Derived Equivalence Classification of Representation-finite Selfinjective Standard Algebras

Derived equivalence classification of one-parametric selfinjective algebras

In continuation of our paper [7] we complete the description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the stable equivalence normal forms of these algebras is obtained. 2000 MSC: Primary: 16G10, 18E30; Secondary: 16D50, 16G60, 16G70.

Flow Equivalence of Graph Algebras

This paper explores the effect of various graphical constructions upon the associated graph C∗-algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that outsplittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C∗-algebras. We generalise the notion of a del...

Graph Algebras and Orbit Equivalence

We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if and only if there is a diagonal-preserving isomorphism between their C∗-algebras. We show that it is necessary to assume that every cycle has an exit for the f...