Symplectic $C_\infty$-algebras

Details Symplectic $C_\infty$-algebras Symplectic $C_\infty$-algebras

2007-07-26

arxiv.org/abs/0707.3951v2

Mathematics

Quantum Algebra

This paper is a substantial revision of the part of math.QA/0410621 dealing with sympectic $C_\infty$-algebras. The main addit

Scientific paper

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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