Stable equivalence of representation-finite trivial extension algebras

Representation Type and Stable Equivalence of Morita Type for Finite Dimensional Algebras

In this note we show that two nite dimensional algebras have the same representation type if they are stably equivalent of Morita type. Stable equivalences of Morita type were introduced for blocks of group algebras by Brou e 2], see also 7]. The concept is motivated by a result of Rickard. In 9], he proved that any derived equivalence between nite dimensional self-injective algebras and ? indu...

The Derived Equivalence Classification of Representation-finite Selfinjective Standard Algebras

On the tameness of trivial extension algebras

For a finite dimensional algebra A over an algebraically closed field, let T (A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if TA is a tilting module and B = EndTA, then T (A) is tame if and only if T (B) is tame. Introduction. Let k be an algebraically closed field. In this paper, an algebra A is always assumed to be associative, with an ide...

Characterizing Tolerance Trivial Finite Algebras

An algebra A is tolerance trivial if Tol A = ConA where Tol A is the lattice of all tolerances on A. If A contains a Mal'cev function compatible with each T Tol A, then A is tolerance trivial. We investigate nite algebras satisfying also the converse statement. Let R be a binary relation on a set A and f be an n-ary function on A. We say that f is compatible with R or that R is compatible with ...

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.