# Minimal models of quantum homotopy Lie algebras via the BV-formalism

## TL;DR

This paper develops an explicit, axiomatic construction of minimal models for quantum L-infinity-algebras using the BV-formalism, with combinatorial formulas and canonical morphisms.

## Contribution

It introduces a novel formal super integral approach to quantum homotopy Lie algebras and constructs inverse morphisms on the homology level.

## Key findings

- Explicit minimal model construction via formal super integrals
- Axiomatic approach enabling perturbation theory techniques
- Existence of canonical morphisms between formal functions on homology and the full space

## Abstract

Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic; they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix. Additionally, there exists a canonical differential graded Lie algebra morphism mapping formal functions on homology to formal functions on the whole space. An L-infinity-algebra morphism inverse to this differential graded Lie algebra morphism on the level of homology is constructed as a formal super integral.