Nakayama functors for Frobenius tensor categories

開催日時
2021/11/25 木 16:00 - 17:30
講演者
清水健一
講演者所属
芝浦工業大
概要

This talk is based on my joint work with Taiki Shibata. The Nakayama functor is an important notion in the representation theory of finite-dimensional algebras. Fuchs, Schaumann, and Schweigert pointed out that the Nakayama functor has a certain universal property and, by using this property, defined the Nakayama functor for finite abelian categories. As they also pointed out, such an abstract treatment of the Nakayama functor turned out to be very useful for proving general results on finite tensor categories.
In this talk, I will explain how and when one can define the Nakayama functor for a locally finite abelian category. Let A be a locally finite abelian category. Technical difficulty is that there is no endofunctor on A satisfying the same universal property as in the finite case. Such an endofunctor on A exists if, for example, A is the category of finite-dimensional comodules over a semiperfect coalgebra. This observation allows us to define the Nakayama functor for Frobenius tensor categories in the sense of Andruskiewitsch, Cuadra and Etingof. Using the Nakayama functor, one can prove some general results on Frobenius tensor categories in the same way as the finite case.

This is a zoom seminar.
Zoom URL: https://us02web.zoom.us/j/87319336585
passcode: The order of the Weyl group of type $E_6$