Yorck Sommerhäuser

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The talk is based on so far unpublished joint work with Yevgenia Kashina.