Crossed modules and quantum groups in braided categories I

1994/08/18 by Yuri Bespalov, Bespalov, Yuri
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/9408102

openalex publication_date 1994/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a Hopf algebra in braided category \cal C. Crossed modules over H are objects with both module and comodule structures satisfying some comatibility condition. Category \cal C^H_H of crossed modules is braided and is concrete realization of general categorical construction. For quantum braided group (H,\cal R) corresponding braided category \cal C^{\cal R}_H of modules is identifyed with full subcategory in \cal C_H^H. Connection with crossproducts is discussed. Correct cross product in the class of quantum braided groups is built. Radford's--Majid's theorem gives equivalent condition for usual Hopf algebra to be crossproduct. Braided variant and analog of this theorem for quantum braided qroups are obtained.

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