Stable Equivalence and Generic Modules.

Let Λ and Γ be finite dimensional algebras. It is shown that any stable equivalence f:mod¯Λ→mod¯Γ between the categories of finitely generated modules induces a bijection M ↦ Mf between the sets of isomorphism classes of generic modules over Λ and Γ such that the endolength of Mf is bounded by the endolength of M up to a scalar which depends only 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. 2000 Mathematics Subject Classification 16G60, 16D90. [ABSTRACT FROM AUTHOR]