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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hochschild cohomology of group extensions of quantum symmetric algebras
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by Deepak Naidu, Piyush Shroff and Sarah Witherspoon PDF
Proc. Amer. Math. Soc. 139 (2011), 1553-1567 Request permission

Abstract:

Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded vector space structure. This yields a complete description of the Hochschild cohomology ring of the corresponding skew group algebra.
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Additional Information
  • Deepak Naidu
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email: dnaidu@math.tamu.edu
  • Piyush Shroff
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email: pshroff@math.tamu.edu
  • Sarah Witherspoon
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 364426
  • Email: sjw@math.tamu.edu
  • Received by editor(s): November 19, 2009
  • Received by editor(s) in revised form: May 14, 2010
  • Published electronically: September 16, 2010
  • Additional Notes: The second and third authors were partially supported by NSF grant #DMS-0800832 and Advanced Research Program Grant 010366-0046-2007 from the Texas Higher Education Coordinating Board.
  • Communicated by: Martin Lorenz
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1553-1567
  • MSC (2010): Primary 16E40, 16S35
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10585-3
  • MathSciNet review: 2763745