On the abstract Bogomolov-Tian-Todorov Theorem

TL;DR

This paper presents an abstract algebraic criterion for determining when differential graded Lie algebras are homotopy abelian, extending the Bogomolov-Tian-Todorov theorem with numerous applications in deformation theory.

Contribution

It introduces a new algebraic criterion for homotopy abelianity of dg Lie algebras, generalizing the classical theorem and unifying various examples and applications.

Findings

Established an algebraic criterion for homotopy abelian dg Lie algebras

Collected multiple examples and applications in deformation theory

Extended the scope of the Bogomolov-Tian-Todorov theorem

Abstract

We describe an abstract version of the Theorem of Bogomolov-Tian-Todorov, whose underlying idea is already contained in various papers by Bandiera, Fiorenza, Iacono, Manetti. More explicitly, we prove an algebraic criterion for a differential graded Lie algebras to be homotopy abelian. Then, we collect together many examples and applications in deformation theory and other settings.