Cohomology Theories of Hopf Bimodules and Cup-Product

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• 作者：Rachel Taillefer (1)
  
• 关键词：cohomology ; Hopf algebras
• 刊名：Algebras and Representation Theory
• 出版年：2004
• 出版时间：December 2004
• 年：2004
• 卷：7
• 期：5
• 页码：471-490
• 全文大小：167KB
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• 作者单位：Rachel Taillefer (1)
  
  1. D茅partement de Math茅matiques CC 051, Laboratoire G.T.A., UPRES A 5030, Universit茅 Montpellier II, 34095, Montpellier Cedex 5, France
  
• ISSN：1572-9079

文摘

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.