Symplectic $C_\infty$-algebras

Alastair Hamilton; Andrey Lazarev

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arXiv · 0707.3951

Symplectic $C_\infty$-algebras

Alastair Hamilton·Andrey Lazarev

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Abstract

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

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BibTeX RIS

Alastair Hamilton, Andrey Lazarev. 2007-07-26. Symplectic $C_\infty$-algebras. https://arxiv.org/abs/0707.3951

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