On the Hochschild cohomology theory of A∞-algebra

Abstract

We will study the simplicial (co)homology for Hochschild complex for A∞–algebra with homotopical properties. The relations which relate a simplicial cohomology of commutative A∞-algebra and the set twisted cochain D(A, A), of this complex holds and studying. A Vanishing Hochschild cohomology for a special degree gives vanishing for the set D(A, A). Finally, we obtained the new extension of a appropriate case for A∞–algebra. Keywords: Cohomology theory, Homotopy, A∞-algebra, MSC: 55N35, 16E40, 14F35