Indecomposables live in all smaller lengths
Representation Theory
2012-01-12 v2 Category Theory
Abstract
Let k be an algebraically closed field and A a finite dimensional associative k-algebra. We prove that there is no gap in the lengths of indecomposable A-modules of finite length. The analogous result holds for an abelian k-linear category C if the endomorphism algebras of the simples are k.
Cite
@article{arxiv.0904.4609,
title = {Indecomposables live in all smaller lengths},
author = {Klaus Bongartz},
journal= {arXiv preprint arXiv:0904.4609},
year = {2012}
}
Comments
correction of an error in part c) of lemma 9; minor changes (style)