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Symplectic C ∞ -algebras.

Research output: Contribution to journalJournal article

Published

Journal publication date2008
JournalMoscow Mathematical Journal
Journal number3
Volume8
Original languageEnglish

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.