Gerstenhaber algebra
= Gerstenhaber algebra
{c}
{wiki}
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.