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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.

The Gerstenhaber bracket as a Schouten bracket for polynomial rings extended by finite groups