Gerstenhaber algebra

Summary

A Gerstenhaber algebra is a graded commutative algebra with a Lie bracket of degree $-1$ that acts on products by the Leibniz rule. Murray Gerstenhaber found this structure on the Hochschild cohomology of an associative algebra. Polyvector fields on a manifold with the Schouten–Nijenhuis bracket form another basic example. It is the graded analogue of a Poisson algebra, with the bracket shifted by one degree.