Exact Borel subalgebras, idempotent quotients and idempotent subalgebras
Representation Theory
2026-04-10 v2 Rings and Algebras
Abstract
This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category having basic regular exact Borel subalgebras.
Keywords
Cite
@article{arxiv.2503.10461,
title = {Exact Borel subalgebras, idempotent quotients and idempotent subalgebras},
author = {Teresa Conde and Julian Külshammer},
journal= {arXiv preprint arXiv:2503.10461},
year = {2026}
}
Comments
27 pages; v2: minor changes, added Remark 3.18 and Example 4.6