Symplectic $C_{\infty }$-algebras

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.

This paper is a substantial revision of the part of math.QA/0410621 dealing with sympectic $C_{\infty }$-algebras. The main addition is the treatment of unital $C_{\infty }$-structures. 27 pages

References in corpus (1)

• Cohomology theories for homotopy algebras and noncommutative geometry