1996/08/23 by Yuri Bespalov, Bespalov, Yuri, Bernhard Drabant +1
Mathematics · Physics and Astronomy · #16W30 #17B37 (Primary) 18D10 (Secondary) #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Bialgebra #Differential (mechanical device) #Division algebra #FOS: Mathematics #Filtered algebra #Generalization #Hopf algebra #Invariant (physics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quasitriangular Hopf algebra #Representation theory of Hopf algebras #math.QA #msc:16W30 #msc:17B37 #msc:18D10 #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9608019
LaTeX, 15 pages
arxiv created 1996/08/23 · openalex publication_date 1996/08/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider Hopf bimodules and crossed modules over a Hopf algebra H in a braided category. They are the key-stones for braided bicovariant differential calculi and their invariant vector fields respectively, as well as for the construction of braided Hopf algebra cross products. We show that the notions of Hopf bimodules and crossed modules are equivalent. A generalization of the Radford-Majid criterion to the braided case is given and it is seen that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. We study the theory of (bicovariant) differential calculi in braided abelian categories and we construct \NN0-graded bicovariant differential calculi out of first order bicovariant differential calculi. These objects are shown to be Hopf algebra differential calculi with universal bialgebra properties in the braided \NN0-graded category.