Generic modules for trivial extension algebras

摘要

Let A be a finite-dimensional algebra over an algebraically closed field. An indecomposable (right) A-module M is called generic provided M is infinite k-dimensional but finite length as (left) End_A(M)-module. Let R = A X DA be the trivial extension algebra of A. Generic R-modules are constructed from generic A-modules using some functors between Mod A and Mod R. It is also proved that if A is a tame hereditary algebra, then R has only two generic modules.