Yetter-Drinfeld modules for Turaev crossed structures

Details Yetter-Drinfeld modules for Turaev crossed structures Yetter-Drinfeld modules for Turaev crossed structures

2002-12-18

arxiv.org/abs/math/0212252v1

Mathematics

Quantum Algebra

latex, 30 pages

Scientific paper

We provide an analog of the Joyal-Street center construction and of the Kassel-Turaev categorical quantum double in the context of the crossed categories introduced by Turaev. Then, we focus or attention to the case of categories of representation. In particular, we introduce the notion of a Yetter-Drinfeld module over a crossed group coalgebra H and we prove that both the category of Yetter-Drinfeld modules over H and the center of the category of representations of H as well as the category of representations of the quantum double of H are isomorphic as braided crossed categories.

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