Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

Details Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

2005-06-28

arxiv.org/abs/math/0506570v2

Mathematics

Quantum Algebra

41 pages, no figures

Scientific paper

10.1007/s00220-006-0051-z

In this paper we introduce generalizations of diagonal crossed products, two-sided crossed products and two-sided smash products, for a quasi-Hopf algebra H. The results we obtain may be applied to H^*-Hopf bimodules and generalized Yetter-Drinfeld modules. The generality of our situation entails that the "generating matrix" formalism cannot be used, forcing us to use a different approach. This pays off because as an application we obtain an easy conceptual proof of an important but very technical result of Hausser and Nill concerning iterated two-sided crossed products.

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