Symplectic C_∞-algebras

2007/07/26 by Hamilton, Alastair, Lazarev, Andrey
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0707.3951

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 \ci-algebra and does not generalize to algebras over other operads.

Related

• Homotopy algebras and noncommutative geometry
• Cyclic BV_∞ algebra and Frobenius manifold
• Calabi-Yau Frobenius algebras
• Homotopy Cartan calculus and inner deformations of A_∞-algebras
• Characteristic classes of A-infinity algebras