A categorical approach to Turaev's Hopf group-coalgebras

Details A categorical approach to Turaev's Hopf group-coalgebras A categorical approach to Turaev's Hopf group-coalgebras

2004-09-30

arxiv.org/abs/math/0409600v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

We show that Turaev's group-coalgebras and Hopf group-coalgebras are coalgebras and Hopf algebras in a symmetric monoidal category, which we call the Turaev category. A similar result holds for group-algebras and Hopf group-algebras. As an application, we give an alternative approach to Virelizier's version of the Fundamental Theorem for Hopf algebras. We introduce Yetter-Drinfeld modules over Hopf group-coalgebras using the center construction.

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