Cohomology theories of Hopf bimodules and cup-product |
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| Institution: | 1. Department of Clinical Sciences, Institute of Tropical Medicine, Antwerp, Belgium;2. WHO Collaborating Centre for Leishmaniasis, Centro Nacional de Microbiologia, Instituto de Salud Carlos III, Ramón y Cajal Hospital, Madrid, Spain;3. Tropical Medicine, Infectious Diseases Department, Ramón y Cajal Hospital, Madrid, Spain |
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| Abstract: | Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf bimodules over A, introduced by Gerstenhaber and Schack, and by Ospel. We prove, when all the spaces involved are finite dimensional, that they are all equal to the Ext functor on the module category of an associative algebra X associated to A, as described by Cibils and Rosso. We also give an expression for a cup-product in the cohomology defined by Ospel, and prove that it corresponds to the Yoneda product of extensions. |
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