Cohomology Theories of Hopf Bimodules and Cup-Product
Identifieur interne : 000299 ( France/Analysis ); précédent : 000298; suivant : 000300Cohomology Theories of Hopf Bimodules and Cup-Product
Auteurs : Rachel Taillefer [France]Source :
- Algebras and Representation Theory [ 1386-923X ] ; 2004-12-01.
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Abstract
Abstract: 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 all 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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DOI: 10.1023/B:ALGE.0000048319.07763.64
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ISTEX:2B0906D16FB86BD3998EA6C9F39DFC9992E4BE7BLe document en format XML
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