In the bocs seat: Quasi-hereditary algebras and representation type

Abstract

This paper surveys bocses, quasi-hereditary algebras and their relationship which was established in a recent result by Koenig, Ovsienko, and the author. Particular emphasis is placed on applications of this result to the representation type of the category filtered by standard modules for a quasi-hereditary algebra. In this direction, joint work with Thiel is presented showing that the subcategory of modules filtered by Weyl modules for tame Schur algebras is of finite representation type. The paper also includes a new proof for the classication of quasi-hereditary algebras with two simple modules, a result originally obtained by Membrillo–Hernández in [70].