Cohomology theories for homotopy algebras and noncommutative geometry

Details Cohomology theories for homotopy algebras and noncommutative geometry Cohomology theories for homotopy algebras and noncommutative geometry

2007-07-26

arxiv.org/abs/0707.3937v1

Mathematics

Quantum Algebra

This 54 pages paper is a substantial revision of the part of math.QA/0410621 dealing with algebraic Hodge decompositions of Ho

Scientific paper

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.

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