Demonet--Iyama--Jasso introduced a new class of finite dimensional algebras, $\tau$-tilting finite algebras. $\tau$-tilting finiteness of algebras relates to brick finiteness, functorially finiteness of torsion classes, and connectivity of silting complexes. In the context of modular representation theory of finite groups, Eisele--Janssens--Raedschelders showed that group algebras of tame type are $\tau$-tilting finite. Given the classical result that the representation type (representation finite, tame, or wild) of group algebras is determined by their $p$-Sylow subgroups, where $p$ denotes the characteristic of the ground field, it is natural to ask what controls $\tau$-tilting finiteness of group algebras. In this talk, we will see that $\tau$-tilting finiteness of group algebras is determined by so-called $p$-hyperfocal subgroups in some cases. This talk is based on a joint work with Yuta Kozakai.

This seminar is a hybrid meeting.

Zoom Meeting ID: 871 0112 0615, Passcode: 004003