1995/10/06 by Yuri Bespalov, Bespalov, Yuri, Bernhard Drabant +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9510009
uuencoded compressed postscript file, 20 pages
arxiv created 1995/10/06 · openalex publication_date 1995/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.