Combinatorics and formal geometry of the master equation

TL;DR

This paper explores the algebraic and geometric structures underlying the master equation in homotopy algebras, focusing on operads, automorphisms, and Maurer-Cartan twisting.

Contribution

It provides a unified framework connecting combinatorics, formal geometry, and homotopy algebra structures for the master equation.

Findings

Operads and geometric objects encode homotopy algebra structures.

Maurer-Cartan twisting corresponds to automorphisms of universal objects.

Framework unifies algebraic and geometric perspectives on the master equation.

Abstract

We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting is encoded in certain automorphisms of these universal objects.