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

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.