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Symplectic C ∞ -algebras.

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>2008
<mark>Journal</mark>Moscow Mathematical Journal
<mark>Original language</mark>English


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.