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 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.

中文翻译：

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一般扭曲张量积的 Hochschild 上同调上的 Gerstenhaber 括号

我们在代数扭曲张量积的 Hochschild 上同调上构建 Gerstenhaber 括号，并作为示例，计算 Buchweitz、Green、Madsen 和 Solberg 工作中出现的一些量子完全交集的 Gerstenhaber 括号。我们证明了扭曲张量积的 Hochschild 上同调环的子代数，其上的扭曲是微不足道的，作为 Gerstenhaber 代数，与因子的 Hochschild 上同调环的各个子代数的张量积同构。