Abstract Hodge decomposition and minimal models for cyclic algebras

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.

First part of Example 2.9 removed. Thanks to Pavel Hajek for spotting a mistake in it

Cited by in corpus (8)

• Quantum $L_{\infty }$ Algebras and the Homological Perturbation Lemma
• Unimodular homotopy algebras and Chern-Simons theory
• Minimal models of quantum homotopy Lie algebras via the BV-formalism
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• On the extension of a TCFT to the boundary of the moduli space
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras
• Hodge decompositions and Poincare duality models
• Ambitwistor Yang-Mills Theory Revisited