Tuesday, July 13, 2021

Tiago Cruz, Quality of split quasi-hereditary covers and Ringel duality.

Abstract:
In this talk, we will explore some split quasi-hereditary covers and their quality. For example, the block algebras of the classical category 𝒪, together with their projective-injective module, are split quasi-hereditary covers of subalgebras of coinvariant algebras. We will talk about a new generalization of relative dominant (and codominant) dimension with respect to a summand of a characteristic tilting module and how this is a tool to the study of split quasi-hereditary covers. Using these concepts we reprove Soergel's theorem that block algebras of the BGG category 𝒪 are Ringel self-dual.