Hochschild cohomology of group extensions of quantum symmetric algebras

Details Hochschild cohomology of group extensions of quantum symmetric algebras Hochschild cohomology of group extensions of quantum symmetric algebras

2009-11-19

arxiv.org/abs/0911.3696v2

Proc. Amer. Math. Soc. 139 (2011), 1553-1567

Mathematics

Rings and Algebras

14 pages; v2: Sections 4 and 5 of v1 merged, minor revisions; to appear in Proc. Amer. Math. Soc

Scientific paper

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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