Strong homotopy inner product of an A-infinity algebra

2007/09/26 by Cho, Cheol-Hyun
#46CXX #53DXX #Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0709.4189

Abstract

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A-infinity algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the notion of a non-constant symplectic structure on the corresponding formal non-commutative supermanifold. We show that (open Gromov-Witten type) potential for a cyclic filtered A-infinity algebra is invariant under the cyclic filtered A-infinity homomorphism up to reparametrization, cyclization and a constant addition, generalizing the work of Kajiura.

Related

• Tensor Products of A_∞-algebras with Homotopy Inner Products
• Infinity inner products on A-infinity algebras
• Infinity-Inner-Products on A-Infinity-Algebras
• Derived A-infinity algebras and their homotopies
• Tensor products of representations up to homotopy