1. Braidings of Tensor Spaces
- Author
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Oleg Ogievetsky, Thomas Grapperon, Centre de Physique Théorique - UMR 6207 (CPT), Centre National de la Recherche Scientifique (CNRS)-Université de Toulon (UTLN)-Université de Provence - Aix-Marseille 1-Université de la Méditerranée - Aix-Marseille 2, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), and Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
010102 general mathematics ,Statistical and Nonlinear Physics ,16. Peace & justice ,Space (mathematics) ,01 natural sciences ,Combinatorics ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Mathematics::Quantum Algebra ,0103 physical sciences ,Mathematics - Quantum Algebra ,[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] ,FOS: Mathematics ,Quantum Algebra (math.QA) ,010307 mathematical physics ,Tensor ,0101 mathematics ,16T25, 81R50, 17B37 ,Mathematical Physics ,Vector space ,Mathematics - Abstract
Let $V$ be a braided vector space, that is, a vector space together with a solution $\hat{R}\in {\text{End}}(V\otimes V)$ of the Yang--Baxter equation. Denote $T(V):=\bigoplus_k V^{\otimes k}$. We associate to $\hat{R}$ a solution $T(\hat{R})\in {\text{End}}(T(V)\otimes T(V))$ of the Yang--Baxter equation on the tensor space $T(V)$. The correspondence $\hat{R}\rightsquigarrow T(\hat{R})$ is functorial with respect to $V$., Comment: 10 pages, no figures
- Published
- 2010
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