Qunhua Liu (Nanjing Normal University)

A dichotomy of algebras with two simples.

Abstract:

By a work of Cline, Parshall and Scott, the derived module category of a quasi-hereditary algebra admits a stratification filtered by vector spaces. We provide a positive answer to the converse question for algebras with two simples, namely, the existence of such a stratification of the derived module category implies the quasi-heredity of the algebra, up to derived equivalence. As a consequence, an algebra with two simples is either derived simple or derived equivalent to a quasi-hereditary algebra. This is a joint work with Dong Yang.