More properties of Yetter-Drinfeld modules over quasi-Hopf algebras

Details More properties of Yetter-Drinfeld modules over quasi-Hopf algebras More properties of Yetter-Drinfeld modules over quasi-Hopf algebras

2003-11-21

arxiv.org/abs/math/0311381v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

We generalize various properties of Yetter-Drinfeld modules over Hopf algebras to quasi-Hopf algebras. The dual of a finite dimensional Yetter-Drinfeld module is again a Yetter-Drinfeld module. The algebra $H_0$ in the category of Yetter-Drinfeld modules that can be obtained by modifying the multiplication in a proper way is quantum commutative. We give a Structure Theorem for Hopf modules in the category of Yetter-Drinfeld modules, and deduce the existence and uniqueness of integrals from it.

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