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Cohomology theories for homotopy algebras and noncommutative geometry · arXivDesk

0707.3937Jul 26, 2007This 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

Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton, Andrey Lazarev

Quantum Algebra Algebraic Geometry K-Theory and Homology

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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

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C_\infty

-algebras. This generalizes and puts in a conceptual framework previous work by Loday and Gerstenhaber-Schack.

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