Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories
q-alg
2008-02-03 v1 Quantum Algebra
Abstract
Hopf (bi-)modules and crossed modules over a bialgebra B in a braided monoidal category C are considered. The (braided) monoidal equivalence of both categories is proved provided B is a Hopf algebra (with invertible antipode). Bialgebra projections and Hopf bimodule bialgebras over a Hopf algebra in C are found to be isomorphic categories. As a consequence a generalization of the Radford-Majid criterion for a braided Hopf algebra to be a cross product is obtained. The results of this paper turn out to be fundamental for the construction of (bicovariant) differential calculi on braided Hopf algebras.
Cite
@article{arxiv.q-alg/9510009,
title = {Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories},
author = {Yuri Bespalov and Bernhard Drabant},
journal= {arXiv preprint arXiv:q-alg/9510009},
year = {2008}
}
Comments
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