Diagonal Crossed Products by Duals of Quasi-Quantum Groups

Details Diagonal Crossed Products by Duals of Quasi-Quantum Groups Diagonal Crossed Products by Duals of Quasi-Quantum Groups

1997-08-04

arxiv.org/abs/q-alg/9708004v1

Physics

High Energy Physics

High Energy Physics - Lattice

75 pages, amslatex

Scientific paper

Let \G be a (weak) quasi-Hopf algebra. Using a two-sided \G-coaction on an algebra \M, we construct what we call the diagonal crossed product as a new associative algebra structure on \M\otimes \dG, where \dG is the dual of \G. This construction is largely motivated by the special case \M = \G, for which we obtain an explicit definition of the quantum double \D(\G) for quasi-Hopf algebras. Applications of our formalism include the field algebra construction of Mack and Schomerus as well as the formulation of Hopf Spin chains or lattice current algebras based on truncated quantum groups at roots of unity. A complete proof that \D(\G) is even a (weak) quasi-triangular quasi-Hopf algebra will be given in a separate paper.

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