Existence of Gradings on Associative Algebras
Representation Theory
2015-05-06 v1 Rings and Algebras
Abstract
In this paper we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra does not have a non-trivial grading if and only if is basic, its quiver has one vertex, and its group of outer automorphisms is unipotent. We apply this result to prove that up to graded Morita equivalence there do not exist non-trivial gradings on the blocks of group algebras with quaternion defect groups and one isomorphism class of simple modules.
Keywords
Cite
@article{arxiv.1505.00934,
title = {Existence of Gradings on Associative Algebras},
author = {Dusko Bogdanic},
journal= {arXiv preprint arXiv:1505.00934},
year = {2015}
}
Comments
We give necessary and sufficient conditions for an associative finite dimensional algebra not to possess a non-trivial Z-grading. arXiv admin note: text overlap with arXiv:1001.1643