Cohomology theories for homotopy algebras and noncommutative geometry

Hamilton, Alastair; Lazarev, Andrey

doi:10.2140/agt.2009.9.1503

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Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton and Andrey Lazarev

Algebraic & Geometric Topology 9 (2009) 1503–1583

DOI: 10.2140/agt.2009.9.1503

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 generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.

Keywords

infinity-algebra, cyclic cohomology, Harrison cohomology, symplectic structure, Hodge decomposition

Mathematical Subject Classification 2000

Primary: 13D03, 13D10

Secondary: 46L87

References

Publication

Received: 2 December 2008

Revised: 31 May 2009

Accepted: 23 June 2009

Published: 1 August 2009

Authors

Alastair Hamilton
Mathematics Department University of Connecticut 196 Auditorium Road Storrs CT 06269-3009 USA
http://www.math.uconn.edu/~hamilton/
Andrey Lazarev
Department of Mathematics University of Leicester Leicester LE1 7RH England
http://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/al179

Volume 9, issue 3 (2009)