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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hochschild cohomology of group extensions of quantum symmetric algebras


Authors: Deepak Naidu, Piyush Shroff and Sarah Witherspoon
Journal: Proc. Amer. Math. Soc. 139 (2011), 1553-1567
MSC (2010): Primary 16E40, 16S35
Published electronically: September 16, 2010
MathSciNet review: 2763745
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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
Email: sjw@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10585-3
PII: S 0002-9939(2010)10585-3
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.