Symplectic $C_\infty$-algebras
Quantum Algebra
2007-07-27 v2 Algebraic Geometry
K-Theory and Homology
Abstract
In this paper we show that a strongly homotopy commutative (or -) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic -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 -algebra and does not generalize to algebras over other operads.
Cite
@article{arxiv.0707.3951,
title = {Symplectic $C_\infty$-algebras},
author = {Alastair Hamilton and Andrey Lazarev},
journal= {arXiv preprint arXiv:0707.3951},
year = {2007}
}
Comments
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