A categorical approach to Turaev's Hopf group-coalgebras
Quantum Algebra
2007-05-23 v1 Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.math/0409600,
title = {A categorical approach to Turaev's Hopf group-coalgebras},
author = {S. Caenepeel and M. De Lombaerde},
journal= {arXiv preprint arXiv:math/0409600},
year = {2007}
}
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22 pages