 Gerstenhaber algebra

A Gerstenhaber algebra has an associative product making it a graded commutative algebra and a degree-minus-one graded Lie bracket. In the left convention, $[u,vw]=[u,v]w+(-1{)}^{(|u|-1)|v|}v[u,w]$. The shifted degrees $|u|-1$ determine the signs of antisymmetry and the Jacobi identity. Hochschild cohomology and the exterior algebra of polynomial derivations are examples.

A **Gerstenhaber algebra** is a type of algebra that arises in the context of deformation theory and algebraic topology. It is named after Marvin Gerstenhaber, who introduced the concept in the 1960s.