Hopf Algebras and Their Generalizations from a Categorical Point of View

Mini course by

Professor Gabriella Böhm

Wigner Research Centre for Physics

Hungarian Academy of Sciences

March 6 - 10, 2017

Picture of Gabriella B&oum;hm

Folklore says that Hopf algebras are distinguished algebras whose representation category admits a closed monoidal structure. In the mini course we will discuss generalizations of bialgebras and Hopf algebras based on this principle.

The first lecture will be used to present the necessary categorical background. The key notion will be the lifting of functors and natural transformations to Eilenberg-Moore categories of monads.

In the second lecture this general theory will be applied to the lifting of the (closed) monoidal structure of a category to the Eilenberg-Moore category of a monad on it. This results in the notions of bimonads and Hopf monads.

In the third lecture, we will first see how the classical structures of bialgebras and Hopf algebras over fields and, more generally, in braided monoidal categories fit into this framework, and then proceed to discuss bialgebroids and Hopf algebroids over an arbitrary base algebra.

The fourth lecture will be devoted to the particular bialgebroids and Hopf algebroids whose base algebra possesses a separable Frobenius structure, known as weak bialgebras or weak Hopf algebras, respectively.

The subject of the fifth lecture will be bimonoids and Hopf monoids in so-called duoidal categories.

The precise schedule of the mini course is

Monday, March 6, 4:30 pm - 6:00 pm, SN 1019

Tuesday, March 7, 3:00 pm - 4:30 pm, C 2004

Wednesday, March 8, 4:30 pm - 6:00 pm, SN 1019

Thursday, March 9, 4:30 pm - 6:00 pm, SN 1019

Friday, March 10, 3:00 pm - 4:30 pm, C 2004

Everyone is invited! We plan to provide partial support for students from Atlantic Canada. Please email a recommendation letter from your supervisor at aac@mun.ca.

Mini Course Materials

Lecture Notes