Symmetric centres of braided monoidal categories |
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| Authors: | CAI Chuanren JIANG Baoxin |
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| Institution: | Department of Mathematics, Yangzhou University, Yangzhou 225002, China |
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| Abstract: | This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
 and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
 and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
 , or equivalently, the braid of
 , whereA is a quantum commutativeH-module algebra |
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| Keywords: | Yetter-Drinfel’ d module braided monoidal category symmetric centre |
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