The Hochschild complex of an algebra or scheme is exhibited as the E1-operadic center of the structure sheaf, and the induced E2-algebra structure recovers the classical Gerstenhaber bracket and cup product.
Kontsevich's wheels and invariant polynomial functions on the dual of L ie algebras
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$\mathbb{E}_2$-algebra structures on the derived center of an algebraic scheme
The Hochschild complex of an algebra or scheme is exhibited as the E1-operadic center of the structure sheaf, and the induced E2-algebra structure recovers the classical Gerstenhaber bracket and cup product.