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arXiv · 0707.3937

Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton·Andrey Lazarev
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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.

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BibTeXRIS

Alastair Hamilton, Andrey Lazarev. 2007-07-26. Cohomology theories for homotopy algebras and noncommutative geometry. https://doi.org/10.2140/agt.2009.9.1503

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