Batalin–Vilkovisky Structure on Hochschild Cohomology of Zigzag Algebra of Type A~1.

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. [ABSTRACT FROM AUTHOR]