Volume 9, issue 3 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton and Andrey Lazarev

Algebraic & Geometric Topology 9 (2009) 1503–1583
Abstract

This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A–, C– and L–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–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