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.