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Symplectic C ∞ -algebras.

Hamilton, Alastair and Lazarev, Andrey (2008) Symplectic C ∞ -algebras. Moscow Mathematical Journal, 8 (3). ISSN 1609-3321

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Abstract

In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to algebras over other operads.

Item Type: Article
Journal or Publication Title: Moscow Mathematical Journal
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: 59744
Deposited By: ep_importer_pure
Deposited On: 05 Nov 2012 11:05
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 12:43
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59744

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