FINITE-GROUP FACTORIZATIONS AND BRAIDING

We compute the quantum double, braiding, and other canonical Hopf alge bra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group X into two subgroups. The represen tations of the quantum double are described by a notion of bicrossed b imodules, generalising the cross modules of Whitehead. We also show th at basis-preserving self-duality structures for the bicrossproduct Hop f algebras are in one-one correspondence with factor-reversing group i somorphisms. The example Z(6)Z(6) is given in detail. We show further that the quantum double D(H) is the twisting of D(X) by a nontrivial q uantum cocycle. (C) 1996 Academic Press, Inc.