On Kontsevich's Hochschild cohomology conjecture
Generalizing a conjecture of Deligne, Kontsevich proposed that there should be a notion of Hochschild cohomology of algebras over the little cube operad (or its chain complex) which in a natural way generalizes Hochschild cohomology of associative algebras. He moreover conjectured that the Hochschild cohomology, in this new sense, of an algebra over the little k-cube operad is an algebra over the little (k + 1)-cube operad. In this paper, we precisely state and prove this conjecture.(Published Online January 13 2006)
(Received March 28 2004)
(Accepted December 8 2004)
Key Words: operads; Hochschild cohomology; algebraic structures.
18D50; 55P48; 13D03.