REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In tau-tilting theory, it is often difficult to determine when a set of bricks is contained in a 2-simple minded collection. For some classes of algebras, this problem reduces to verifying a pairwise condition; namely, the bricks need only satisfy certain conditions on their Hom- and Ext-groups. Curiously, such pairwise characterizations do not hold in general, even for tau-tilting finite algebras. In this talk, we will recall the definition of 2-simple minded collections and their relationship to torsion classes, stability conditions, and c-vectors. We will then consider examples and non-examples of tau-tilting finite algebras whose 2-simple minded collections are characterized by pairwise conditions. This is based on joint works with Emily Barnard and Kiyoshi Igusa.