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.
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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, . The shifted degrees determine the signs of antisymmetry and the Jacobi identity. Hochschild cohomology and the exterior algebra of polynomial derivations are examples.