✦ LIBER ✦

Finite Group Factorizations and Braiding

✍ Scribed by E.J. Beggs; J.D. Gould; S. Majid

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 354 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0112

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✦ Synopsis

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 X 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 basis-preserving self-duality structures for the bicrossproduct Hopf algebras are in one᎐one correspondence with factorreversing group isomorphisms. The example ‫ޚ‬ ‫ޚ‬ is given in detail. We show 6 6

Ž .

Ž . further that the quantum double D H is the twisting of D X by a nontrivial quantum cocycle.

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