MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

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Funded by The Danish National Research Foundation

Geometric Mathematical Physics Seminar

Abstract
We discuss the definition of both crossed group coalgebras and crossed group categories introduced by Turaev for topological motivation. The first is a generalisation of the standard notion of a Hopf algebra, the second of a tensor category. Quasitrinagular structures have an analog in this context. For crossed group coalgebras, we provide an analog of Drinfeld quantum double construction. In that way, starting from a crossed coalgebra H, we obtain a quasitriangular crossed coalgebra D(H). For crossed group categories, we provide an analog of Drinfeld and Joyal - Street center construction: starting from a crossed category C, we obtain a braided crossed category Z(C). We consider the case C=Rep(H). By introducing the category YD(H) of Yetter-Drinfeld modules over H, we prove the isomorphism Rep(D(H))=YD(H)=Z(Rep(H)).

Contact person:Jørgen Ellegaard Andersen.