Stable equivalence and generic modules

Henning Krause and Grzegorz Zwara

Abstract. Let $\Lambda$ and $\Gamma$ be finite dimensional algebras. It is
shown that any stable equivalence $f\colon\overline\mod\Lambda \rightarrow
\overline\mod\Gamma$ between the categories of finitely generated modules
induces a bijection $M \rightarrow M_f$ between the sets of isomorphism
classes of generic modules over $\Lambda$ and $\Gamma$ such that the
endolength of $M_f$ is bounded by the endolength of $M$ up to a scalar which
only depends on $f$. Using Crawley-Boevey's characterization of tame
representation type in terms of generic modules, one obtains as a 
consequence a new proof for the fact that a stable equivalence preserves
tameness. This proof also shows that polynomial growth is preserved.