On the abstract 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.