dorsal/arxiv
View SchemaHopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories
| Authors | Yuri Bespalov, Bernhard Drabant |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9510009 |
| URL | https://arxiv.org/abs/q-alg/9510009 |
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.
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"abstract": "Hopf (bi-)modules and crossed modules over a bialgebra B in a braided\nmonoidal category C are considered. The (braided) monoidal equivalence of both\ncategories is proved provided B is a Hopf algebra (with invertible antipode).\nBialgebra projections and Hopf bimodule bialgebras over a Hopf algebra in C are\nfound to be isomorphic categories. As a consequence a generalization of the\nRadford-Majid criterion for a braided Hopf algebra to be a cross product is\nobtained. The results of this paper turn out to be fundamental for the\nconstruction of (bicovariant) differential calculi on braided Hopf algebras.",
"arxiv_id": "q-alg/9510009",
"authors": [
"Yuri Bespalov",
"Bernhard Drabant"
],
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"title": "Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories",
"url": "https://arxiv.org/abs/q-alg/9510009"
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