September 15, 2026, 10:30 +0200
Padova, Torre Archimede 1C150

Borel subalgebras in highest weight settings

Teresa Conde, Universität Bielefeld

Abstract

Borel subalgebras play an important role in Lie theory, where induction of 1-dimensional modules produces Verma modules and underlies the highest-weight structure of category $\mathcal{O}$. Exact Borel subalgebras of quasi-hereditary algebras are a finite-dimensional analogue. In this talk, I will discuss existence and uniqueness questions for exact Borel subalgebras and explain how these can sometimes be answered through numerical and homological data. I will also describe more recent developments, including joint work with J. Külshammer showing that exact Borel subalgebras behave well under suitable idempotent reductions, and joint work with G. Dalezios and S. Koenig characterising Reedy algebras through PBW-type triangular decompositions.