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

## 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 |
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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: | 05 Feb 2016 00:05 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/59744 |

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