Module and Hochschild cohomology of certain semigroup algebras

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• 作者：A. Shirinkalam ; A. Pourabbas ; M. Amini
• 关键词：module cohomology group ; Hochschild cohomology group ; inverse semigroup ; semigroup algebra
• 刊名：Functional Analysis and Its Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：49
• 期：4
• 页码：315-318
• 全文大小：138 KB
• 参考文献：[1]M. Amini, A. Bodaghi, and D. Ebrahimi Bagha, Semigroup Forum, 80:2 (2010), 302-12.CrossRef MathSciNet MATH
  [2]H. G. Dales, Banach Algebras and Automatic Continuity, Clarendon Press, Oxford, 2000.MATH
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  [10]R. A. Ryan, Introduction to Tensor Products of Banach Spaces, Springer-Verlag, London, 2002.CrossRef MATH
  
• 作者单位：A. Shirinkalam (1)
  A. Pourabbas (2)
  M. Amini (3)
  
  1. Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
  2. Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
  3. Department of Mathematics, Tarbiat Modares University School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Functional Analysis
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8485

文摘

We study the relation between the module and Hochschild cohomology groups of Banach algebras.We show that, for every commutative Banach A-A-bimodule X and every k ?N, the seminormed spaces H _A k (A,X*) and H k (A /J,X*) are isomorphic, where J is a specific closed ideal of A. As an example, we show that, for an inverse semigroup S with the set of idempotents E, where ?sup>1(E) acts on ?sup>1(S) by multiplication on the right and trivially on the left, the first module cohomology \(H_{{\ell ^1}\left( E \right)}^1\) (?sup>1(S), ?sup>1(G _S )(2n+1)) is trivial for each n ?N, where G _S is the maximal group homomorphic image of S. Also, the second module cohomology \(H_{{\ell ^1}\left( E \right)}^2\) (?sup>1(S), ?sup>1(G _S )(2n+1)) is a Banach space. Keywords module cohomology group Hochschild cohomology group inverse semigroup semigroup algebra