Ferrara - 2024
Memorial University of Newfoundland
Self-Duality of Yetter-Drinfel'd Hopf Algebras and Their Biproducts
The dual of a left Yetter-Drinfel'd Hopf algebra is a right Yetter-Drinfel'd Hopf algebra. By transporting these new structures from the right to the left via an antipode or an inverse antipode, this dual can be turned into a left Yetter-Drinfel'd Hopf algebra, which is the left or right dual in the sense of category theory.
For the Yetter-Drinfel'd Hopf algebras constructed by Yevgenia Kashina and the speaker, we show that the arising duals are isomorphic to the original Yetter-Drinfel'd Hopf algebra.
As a consequence, we show that the arising Radford biproducts are also self-dual.
Furthermore, we give an explicit description of the irreducible representations of these biproducts.
The talk is based on so far unpublished joint work with Yevgenia Kashina.