The Gerstenhaber Bracket as a Schouten Bracket for Polynomial Rings Extended by Finite Groups Cris Negron and Sarah Witherspoon
نویسنده
چکیده
We apply new techniques to compute Gerstenhaber brackets on the Hochschild cohomology of a skew group algebra formed from a polynomial ring and a finite group (in characteristic 0). We show that the Gerstenhaber brackets can always be expressed in terms of Schouten brackets on polyvector fields. We obtain as consequences some conditions under which brackets are always 0, and show that the Hochschild cohomology is a graded Gerstenhaber algebra under the codimension grading, strengthening known results.
منابع مشابه
An Alternate Approach to the Lie Bracket on Hochschild Cohomology Cris Negron and Sarah Witherspoon
We define Gerstenhaber’s graded Lie bracket directly on complexes other than the bar complex, under some conditions, resulting in a practical technique for explicit computations. The Koszul complex of a Koszul algebra in particular satisfies our conditions. As examples we recover the Schouten-Nijenhuis bracket for a polynomial ring and the Gerstenhaber bracket for a group algebra of a cyclic gr...
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