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Journal of Noncommutative Geometry

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Volume 11, Issue 4, 2017, pp. 1351–1379
DOI: 10.4171/JNCG/11-4-4

Published online: 2017-12-15

Gerstenhaber brackets on Hochschild cohomology of twisted tensor products

Lauren Grimley[1], Van C. Nguyen[2] and Sarah Witherspoon[3]

(1) Spring Hill College, Mobile, USA
(2) Hood College, Frederick, USA
(3) Texas A&M University, College Station, USA

We construct the Gerstenhaber bracket on Hochschild cohomology of a twisted tensor product of algebras, and, as examples, compute Gerstenhaber brackets for some quantum complete intersections arising in the work of Buchweitz, Green, Madsen, and Solberg.We prove that a subalgebra of the Hochschild cohomology ring of a twisted tensor product, on which the twisting is trivial, is isomorphic, as a Gerstenhaber algebra, to the tensor product of the respective subalgebras of the Hochschild cohomology rings of the factors.

Keywords: Hochschild cohomology, Gerstenhaber brackets, twisted tensor products, quantum complete intersections

Grimley Lauren, Nguyen Van, Witherspoon Sarah: Gerstenhaber brackets on Hochschild cohomology of twisted tensor products. J. Noncommut. Geom. 11 (2017), 1351-1379. doi: 10.4171/JNCG/11-4-4