Homological Perturbation Theory Hochschild Homology and Formal Groups
نویسنده
چکیده
As Don Schack mentioned in his plenary talk [SDS], Gerstenhaber [MG] observed that if A is an associative algebra, then the Hochschild cohomology of A is a graded commutative algebra with an additional structure, viz., that of a Lie algebra. The two structures satisfy a compatibility condition (graded Poission structure). We agree to call such structures G–algebras (Gerstenhaber–algebras). Schack pointed out that if A is a smooth K-algebra, and we give the exterior algebra ΛH0(A,A)(H (A,A)) the NijenhuisSchouten bracket, making it into a G-algebra, we have the classic theorem of Hochschild, Kostant, and Rosenberg (§5): There is an isomorphism of G-algebras
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