Cohomology of Hopf Bimodules and Cup-product

Details Cohomology of Hopf Bimodules and Cup-product Cohomology of Hopf Bimodules and Cup-product

2000-05-02

arxiv.org/abs/math/0005019v2

Mathematics

Quantum Algebra

19pages, submitted to "Algebras and Representation Theory"

Scientific paper

10.1016/S0764-4442(00)01811-5

Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf bimodules over A, introduced by M. Gerstenhaber and S.D. Schack, and by C. Ospel. We prove, when A is finite dimensional, that they are equal to the Ext functor on the module category of an associative algebra associated to A, described by C. Cibils and M. Rosso. We also give an expression for a cup-product in the cohomology defined by C. Ospel, and prove that it corresponds to the Yoneda product of extensions.

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