Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy. J. Chuang is supported by an EPSRC advanced research fellowship. A. Lazarev is partially supported by an EPSRC research grant.