## University of Sydney Algebra Seminar

# Brian Parshall (University of Virginia)

## Friday 23 May, 12:05-12:55pm, Place: 373

### Q-Koszul algebras and three conjectures

Certain types of finite dimensional algebras play an important role in the representation theory of algebraic groups. These include cellular algebras, Koszul and quasi-hereditary algebras. Q-Koszul algebras were introduced very recently by the speaker and Leonard Scott. They have been shown to "model" module categories for semisimple groups in large characteristic. Remarkably, it seems possible that the model extends to small characteristics as well. This includes even p=2 in some cases. This talk surveys Q-Koszul algebras:they can be viewed as interesting objects in their own right and they have connections with the modular representation theory of semisimple groups.