Derived equivalence classification of one-parametric selfinjective algebras

Ju l 2 00 5 Derived Equivalence Classification of Nonstandard Selfinjective Algebras of Domestic Type

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained.

The Derived Equivalence Classification of Representation-finite Selfinjective Standard Algebras

On a Lift of an Individual Stable Equivalence to a Standard Derived Equivalence for Representation-finite Selfinjective Algebras

We shall show that every stable equivalence (functor) between representation-finite selfinjective algebras not of type (D3m, s/3, 1) with m ≥ 2, 3 s lifts to a standard derived equivalence. This implies that all stable equivalences between these algebras are of Morita type.

Stable Calabi-yau Dimension for Finite Type Selfinjective Algebras

We show that the Calabi-Yau dimension of the stable module category of a selfinjective algebra of finite representation type is determined by the action of the Nakayama and suspension functors on objects. Our arguments are based on recent results of C. Amiot, and hence apply more generally to triangulated categories having only finitely many indecomposable objects. Throughout, k is an algebraic...

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...