Homotopy transfer for L-infinity structures and the BV-formalism

TL;DR

This paper develops explicit methods for constructing minimal models of L-infinity algebras using BV-formalism, connecting homotopy transfer, rooted trees, and Feynman diagrams in a mathematical physics context.

Contribution

It provides explicit formulas for minimal models of L-infinity algebras via BV-formalism, illustrating their relation to homotopy transfer and Feynman diagrams.

Findings

Explicit minimal model formulas for L-infinity algebras

Connection between rooted trees and Feynman diagrams

Application of BV-formalism to algebraic structures

Abstract

Explicit constructions for the minimal models of general and unimodular L-infinity algebra structures are given using the BV-formalism of mathematical physics and the perturbative expansions of integrals. In particular, the general formulas for the minimal model of an L-infinity algebra structure are an instance of the Homotopy Transfer Theorem and we recover the known formulas of the structure in terms of sums over rooted trees discussing their relation to Feynman diagrams.