Session S16 - Quantum symmetries

Friday, July 16, 15:30 ~ 15:55 UTC-3

New Examples of Semisimple Hopf Algebras

Yorck Sommerhäuser

Memorial University of Newfoundland, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In joint work with Yevgenia Kashina, the speaker recently constructed two series of Yetter-Drinfel'd Hopf algebras over the Klein four-group in order to refute certain conjectures. All algebras in these series have dimension 8 and depend on a not necessarily primitive fourth root of unity. The algebras in the first series are commutative, while the algebras in the second series are noncommutative.

Via the Radford biproduct construction, these Yetter-Drinfel'd Hopf algebras give rise to semisimple Hopf algebras of dimension 32 that appear not to have been considered in the literature before. We discuss the properties of these Hopf algebras and discuss in particular how many non-isomorphic Hopf algebras arise in this way. For example, it turns out that the biproducts coming from the second series are isomorphic to biproducts coming from the first series.

Joint work with Yevgenia Kashina (DePaul University, USA).

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