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Some Remarks on Braided Group Reconstruction and Braided Doubles

S. Majid
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Abstract

The cross coproduct braided group $Aut(C) \rcocross B$ is obtained by Tannaka-Krein reconstruction from $C^B\to C$ 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 $C^\circ\to C$. General braided double crossproducts $B\dcross C$ are also considered.

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S. Majid. 1998-10-06. Some Remarks on Braided Group Reconstruction and Braided Doubles. https://arxiv.org/abs/math/9810038

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