Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Koszul duality and homotopy theory of curved Lie algebras
AU - Maunder, James
PY - 2017/6/6
Y1 - 2017/6/6
N2 - 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.
AB - 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.
KW - curved Lie algebra
KW - homotopy
KW - Koszul duality
KW - deformation functor
U2 - 10.4310/HHA.2017.v19.n1.a16
DO - 10.4310/HHA.2017.v19.n1.a16
M3 - Journal article
VL - 19
SP - 319
EP - 340
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
SN - 1532-0073
IS - 1
ER -