Hochschild cohomology of group extensions of quantum symmetric algebras

Naidu, Deepak; Shroff, Piyush; Witherspoon, Sarah

doi:10.1090/S0002-9939-2010-10585-3

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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