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Cohomology theories for homotopy algebras and noncommutative geometry

Hamilton, Alastair and Lazarev, Andrey (2009) Cohomology theories for homotopy algebras and noncommutative geometry. Algebraic and Geometric Topology, 9 (3). pp. 1503-1583. ISSN 1472-2747

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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.

Item Type: Article
Journal or Publication Title: Algebraic and Geometric Topology
Uncontrolled Keywords: infinity-algebra ; cyclic cohomology ; Harrison cohomology ; symplectic structure ; Hodge decomposition
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 60053
Deposited By: ep_importer_pure
Deposited On: 16 Nov 2012 15:01
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 12:45
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/60053

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