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Some Remarks on Braided Group Reconstruction and Braided Doubles

1998/10/06 by Shahn Majid, S. Majid, Majid, S.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9810038

Latex 12 pages + epsf figures

arxiv created 1998/10/06 · openalex publication_date 1998/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The cross coproduct braided group Aut(C) \rcocross B is obtained by Tannaka-Krein reconstruction from CB→ C for a braided group B in braided category C. We apply this construction to obtain partial solutions to two problems in braided group theory, namely the tensor problem and the braided double. We obtain Aut(C)\rcocross Aut(C)\isom Aut(C)\lcross Aut(C) and higher braided group `spin chains'. The example of the braided group B(R)\lcross B(R)\lcross...\lcross B(R) is described explicitly by R-matrix relations. We also obtain Aut(C)\rcocross Aut(C)^* as a dual quasitriangular `codouble' braided group by reconstruction from the dual category C^∘→ C. General braided double crossproducts B\dcross C are also considered.

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