Finite Group Factorisations and Braiding

Details Finite Group Factorisations and Braiding Finite Group Factorisations and Braiding

1995-03-30

arxiv.org/abs/q-alg/9503018v1

Mathematics

Quantum Algebra

LATEX, 39 pages, more final version

Scientific paper

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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