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Koszul duality and homotopy theory of curved Lie algebras

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>6/06/2017
<mark>Journal</mark>Homology, Homotopy and Applications
Issue number1
Number of pages22
Pages (from-to)319-340
Publication StatusPublished
<mark>Original language</mark>English


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.