Batalin–Vilkovisky Structure on Hochschild Cohomology of Zigzag Algebra of Type 𝐀_1
Results in Mathematics（2022）
Abstract
In this paper, we study the Batalin–Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras A_𝔮 of type 𝐀_1 . We first calculate the dimensions of Hochschild homology groups and Hochschild cohomology groups of A_𝔮 . Based on these computations, we determine the Hochschild cohomology ring of A_𝔮 , and give the Batalin-Vilkovisky operator and the Gerstenhaber bracket on Hochschild cohomology ring of A_𝔮 explicitly.
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Key words
Batalin–Vilkovisky structure,hochschild (co)homology,zigzag algebras,Gerstenhaber bracket product
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