Finite Group Factorisations and Braiding

E. Beggs; J. Gould; S. Majid

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arXiv · q-alg/9503018

Finite Group Factorisations and Braiding

E. Beggs·J. Gould·S. Majid

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Abstract

We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra $H$ associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that self-duality structures for the bicrossproduct Hopf algebras are in one-one correspondence with factor-reversing group isomorphisms. The example $Z_6Z_6$ is given in detail. We show further that the quantum double $D(H)$ is the twisting of $D(X)$ by a non-trivial quantum cocycle, where $X$ is the associated double cross product group.

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BibTeX RIS

E. Beggs, J. Gould, S. Majid. 1995-03-30. Finite Group Factorisations and Braiding. https://arxiv.org/abs/q-alg/9503018

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