The Gerstenhaber bracket of Hochschild cohomology of triangular quadratic monomial algebra

Hochschild cohomology of group extensions of quantum complete intersections

“…While the algebra structure of Hochschild cohomology of quantum complete intersections with respect to the cup product has been studied, Hochschild cohomology of an associative algebra also admits a graded Lie bracket which is less understood. The graded Lie algebra structure on Hochschild cohomology has been studied for monomial algebras [7,21,23], skew group algebras [22], tensor products [12], group extensions of polynomial rings [19] and skew polynomial rings [25], and the quantum complete intersections Λ (2,2) q [10]. Most recently in [2], Benson, Kessar, and Linkelman studied the Lie algebra structure of the first Hochschild cohomology k-module of Λ (p,p) q for a prime p and q of order dividing p − 1.…”

Polyvector fields for Fano 3-folds

“…Relation to other works. In the representation theory of finite-dimensional algebras the Gerstenhaber algebra structure on Hochschild cohomology is an important invariant, studied in many cases, see [1,14,49,51] to name a few. In algebraic geometry there are (at the time of writing) fewer attempts at giving explicit descriptions of Hochschild cohomology and the Hochschild-Kostant-Rosenberg decomposition.…”