Geometric Characterization of a Class of Modular Representations.

摘要

The purpose of this paper is to prove the following characterization of the invertible elements of the Green ring of a p-elementary Abelian group. Let G=(Z/p)/sup m/, and let k be an algebraically closed field of characteristic p. Suppose M is a finitely generated indecomposable kG-module and let N be a kG-module such that Mx/sub k/N is stably isomorphic to k (with the trivial G-action). Then M is kG-isomorphic to a Heller module omega /sup n/(k), n is an element of Z. In particular, we recover a theorem of E. Dade on the characterization of endo-trivial modules as a corollary. If End/sub k/(M) approx.= k + Free and M is indecomposable, then M approx.= omega /sup n/(k) for some n is an element of Z. (author). 10 refs. (Atomindex citation 19:101765)