Algebra Seminar: Exact Borel subalgebras of quasi-hereditary monomial algebras

Abstract: Given a quasi-hereditary algebra A with an exact Borel subalgebra B, one may use B to study A. However, quasi-hereditary algebras in general do not have exact Borel subalgebras, and while a theorem by König, Külshammer and Ovsienko shows that there always exists a Morita equivalent quasi-hereditary algebra admitting an exact Borel subalgebra, this is by no means easy to calculate explicitly.

In this talk, I would therefore like to restrict this question to the case where A is a quasi-hereditary monomial algebra. Under this assumption, it is possible to use elementary methods in order to show that A always admits an exact Borel subalgebra B, and give an explicit description of B in terms of paths.

Join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.