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Kontsevich and Soibelman has proved a relation between a non-degeneratecyclic homology element of an A-infinity algebra A and its cyclic innerproducts on the minimal model of A. We find an explicit formula of thiscorrespondence, in terms of the strong homotopy inner products and negativecyclic cohomology of A. We prove that an equivalence class of the inducedstrong homotopy inner product depends only on the given negative cycliccohomology class. Also, we extend such a correspondence to the case of gappedfiltered A-infinity algebras.

Notes on Kontsevich-Soibelman's theorem about cyclic A-infinity algebras