Koszul duality and homotopy theory of curved Lie algebras

Abstract

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic zero---Quillen equivalent to a model category of pseudo-compact unital commutative differential graded algebras; this extends known results regarding the Koszul duality of unital commutative differential graded algebras and differential graded Lie algebras. As an application of the theory developed within this paper, algebraic deformation theory is extended to functors on pseudo-compact, not necessarily local, commutative differential graded algebras.

21 pages. The document contains a section recalling details from 1403.0774 (by different authors) to establish notation and make the document as self-contained as possible. This version is a substantial revision of the previous version, making it more readable

References in corpus (3)

• Deformation theory via differential graded Lie algebras
• Deformation theory and rational homotopy type
• Operads and moduli spaces

Cited by in corpus (4)

• Minimal models of quantum homotopy Lie algebras via the BV-formalism
• Relative nonhomogeneous Koszul duality
• Curved Koszul duality of algebras over unital versions of binary operads
• Courant algebroid lifts and curved Courant algebroids