University of Sydney Algebra Seminar

Edmund Heng

Friday 25 September, 12-1pm, in SMRI Seminar Room (Macleay Building A12 Room 301)

A remarkable subcategory of modules using tensor symmetry

We often use group symmetries to study mathematical objects we care about. I’d like to convince you that one can do better using generalised symmetries encoded by tensor categories. In this talk I will be focusing on the representation theory of finite dimensional algebras. Specifically, through the action of a tensor category, I will introduce a subcategory of modules which captures a surprising amount of information of the whole category of modules. In particular, it allows one to compute the finitistic dimension, and answer a question posed by Geiss—Leclerc—Schroer about rigid modules. This will be based on upcoming joint works with Kevin Coulembier and Calvin Pfeifer.