Quantum Groupoids and their Hopf Cyclic Cohomology

Details Quantum Groupoids and their Hopf Cyclic Cohomology Quantum Groupoids and their Hopf Cyclic Cohomology

2011-07-29

arxiv.org/abs/1108.0030v1

Mathematics

Quantum Algebra

48 pages

Scientific paper

We define \times-Hopf coalgebras as a quantization of groupoids. We develop Hopf cyclic theory with coefficients in stable-anti-Yetter-Drinfeld modules for \times-Hopf coalgebras. We use \times-Hopf coalgebras to study coextensions of coalgebras. Finally, we define equivariant \times-Hopf coalgebra coextensions and apply them as functors between categories of stable anti-Yetter-Drinfeld modules over \times-Hopf coalgebras involved in the coextension.

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