Geodesic
Koszul duality and homotopy theory of curved Lie algebras
Homology, homotopy, and applications, Tome 19 (2017) no. 1, pp. 319-340.

Voir la notice de l'article provenant de la source International Press of Boston

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a model 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; extending 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 over pseudo-compact, not necessarily local, commutative differential graded algebras. Further, these deformation functors are shown to be representable.
DOI : 10.4310/HHA.2017.v19.n1.a16
Classification : 18G55, 55U99
Keywords: curved Lie algebra, homotopy, Koszul duality, deformation functor 
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James Maunder. Koszul duality and homotopy theory of curved Lie algebras. Homology, homotopy, and applications, Tome 19 (2017) no. 1, pp. 319-340. doi : 10.4310/HHA.2017.v19.n1.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n1.a16/

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