Algebra Seminar: Jacobson radicals and tensor categories
- Date: 25 February 2025, 15:15–17:00
- Location: Ångström Laboratory, 64119 + Zoom
- Type: Seminar
- Lecturer: Mateusz Stroinski (Uppsala)
- Organiser: Matematiska institutione
- Contact person: Volodymyr Mazorchuk
Mateusz Stroinski gives this seminar. Welcome to join!
Abstract: Finite module categories over a finite tensor category C correspond bijectively to Morita equivalence classes of algebra objects in C. A particularly important class of module categories is that of exact module categories. I will define a Jacobson radical J(A) of an algebra object A in C, and use it to show that A is semisimple if and only if mod(A) is an exact C-module category.
This result was conjectured by Etingof and Ostrik in their work towards a positive-characteristic extension of Deligne's description of symmetric tensor categories via affine (pro)algebraic (super)groups. I will describe this context for the result, and, time allowing, also give further applications. This talk is based on joint work with Kevin Coulembier and Tony Zorman.
Join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)
This is a seminar in our algebra seminar series.