Sufficient and necessary conditions for hereditary of infinite category algebras
Representation Theory
2020-09-14 v2 Group Theory
Rings and Algebras
Abstract
We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension of a category algebra equals the maximal left global dimension of the endomorphism algebras of its objects, and classify its projective modules in this case. As applications, we completely classify transporter categories, orbit categories, and Quillen categories with left hereditary category algebras over a field.
Keywords
Cite
@article{arxiv.2004.08251,
title = {Sufficient and necessary conditions for hereditary of infinite category algebras},
author = {Malte Lackmann and Liping Li},
journal= {arXiv preprint arXiv:2004.08251},
year = {2020}
}
Comments
Some small changes as well as a new appendix