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Symplectic C ∞ -algebras.

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Symplectic C ∞ -algebras. / Hamilton, Alastair; Lazarev, Andrey.
In: Moscow Mathematical Journal, Vol. 8, No. 3, 2008.

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Hamilton A, Lazarev A. Symplectic C ∞ -algebras. Moscow Mathematical Journal. 2008;8(3).

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Hamilton, Alastair ; Lazarev, Andrey. / Symplectic C ∞ -algebras. In: Moscow Mathematical Journal. 2008 ; Vol. 8, No. 3.

Bibtex

@article{0651592039df47a299effe5b11d754e9,
title = "Symplectic C ∞ -algebras.",
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.",
keywords = "Infinity-algebra, cyclic cohomology , Harrison cohomology , symplectic structure , Hodge decomposition",
author = "Alastair Hamilton and Andrey Lazarev",
year = "2008",
language = "English",
volume = "8",
journal = "Moscow Mathematical Journal",
issn = "1609-3321",
publisher = "Independent University of Moscow",
number = "3",

}

RIS

TY - JOUR

T1 - Symplectic C ∞ -algebras.

AU - Hamilton, Alastair

AU - Lazarev, Andrey

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Infinity-algebra

KW - cyclic cohomology

KW - Harrison cohomology

KW - symplectic structure

KW - Hodge decomposition

M3 - Journal article

VL - 8

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

SN - 1609-3321

IS - 3

ER -