Cohomology theories for homotopy algebras and noncommutative geometry

Abstract

This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely $A_{\infty },C_{\infty }$ and $L_{\infty }$-algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of $C_{\infty }$-algebras. This generalizes and puts in a conceptual framework previous work by Loday and Gerstenhaber-Schack.

This 54 pages paper is a substantial revision of the part of math.QA/0410621 dealing with algebraic Hodge decompositions of Hochschild and cyclic cohomology theories. The main addition is the treatment of cohomology theories corresponding to unital infinity-structures

References in corpus (1)

• Transferring homotopy commutative algebraic structures

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