Examples
- Gerstenhaber showed that the Hochschild cohomology H*(A,A) of a graded algebra A is a Gerstenhaber algebra.
- A Batalin–Vilkovisky algebra has an underlying Gerstenhaber algebra if one forgets its second order Δ operator.
- The exterior algebra of a Lie algebra is a Gerstenhaber algebra.
- The differential forms on a Poisson manifold form a Gerstenhaber algebra.
- The multivector fields on a manifold form a Gerstenhaber algebra using the Schouten–Nijenhuis bracket
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