1995/10/12 by Yu. N. Bespalov, Yu . N. Bespalov, Bespalov, Yu. N.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9510013
54 pages, latex, 28 figures prepared by latex This is a completely revised and complemented version of hep-th/9408102,hep-th/9408106 submitted to {\it Appl. Categorical Structures}
arxiv created 1995/10/12 · openalex publication_date 1995/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a Hopf algebra in a braided category \cal C. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category \DY\cal CAA of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group (A, A,\cal R) the corresponding braided category of modules \cal C_\cOA, A is identified with a full subcategory in \DY\cal CAA. The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid--Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.