Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types

TL;DR

This paper constructs Lie algebras of derivations to model moduli spaces of rational homotopy types, linking algebraic derivations with geometric realizations of homotopy classes.

Contribution

It introduces a novel approach to describe moduli spaces of rational homotopy types using Lie algebras of derivations and their Maurer-Cartan sets.

Findings

Lie algebras of derivations are constructed and geometrically realized.

Maurer-Cartan sets classify homotopy types sharing algebraic invariants.

The framework connects algebraic derivations with geometric moduli spaces.

Abstract

We construct Lie algebras of derivations (and identify their geometrical realization) whose Maurer-Cartan sets provide moduli spaces describing the classes of homotopy types of rational spaces sharing either the same homotopy Lie algebra, homology or cohomology.