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.
Action of the Grothendieck-Teichmueller group on the operad of Gerstenhaber algebras
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abstract
Action of the graded Grothendieck-Teichmueller (GT) group on a resolution of the operad of Gerstenhaber algebras (GA) is defined. It is shown that the induced Lie algebra action is homotopically non-trivial (i.e. the induced map from the Lie algebra of the graded GT group to the deformation complex of the operad of GA is injective).
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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.