Abstract Hodge decomposition and minimal models for cyclic algebras

TL;DR

This paper demonstrates that cyclic operad algebras with a Hodge decomposition have unique minimal models constructed via tree summations, advancing the understanding of their homotopy structures.

Contribution

It introduces a method to construct minimal models for cyclic operad algebras with Hodge decompositions, establishing their uniqueness up to homotopy.

Findings

Minimal models are given by summation over trees.

Uniqueness of the minimal model up to homotopy.

Extension of Hodge decomposition to algebraic minimal models.

Abstract

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.