Memorial University of Newfoundland
Atlantic Association for Research in the Mathematical Sciences
Atlantic Algebra Centre
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
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 firstname.lastname@example.org.
Mini Course Materials