Exact Borel subalgebras of quasi-hereditary monomial algebras

2025/04/02 by Rasmussen, Anna Rodriguez
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.01706

Abstract

Green and Schroll give an easy criterion for a monomial algebra A to be quasi-hereditary with respect to some partial order ≤_A. A natural follow-up question is under which conditions a monomial quasi-hereditary algebra (A, ≤_A) admits an exact Borel subalgebra in the sense of König. In this article, we show that it always admits a Reedy decomposition consisting of an exact Borel subalgebra B, which has a basis given by paths, and a dual subalgebra. Moreover, we give an explicit description of B and show that it is the unique exact Borel subalgebra of A with a basis given by paths. Additionally, we give a criterion for when B is regular, using a criterion by Conde.

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