Home > Research > Publications & Outputs > Koszul duality and homotopy theory of curved Li...

Research

Associated organisational unit

Links

Text available via DOI:

Keywords

View graph of relations

Koszul duality and homotopy theory of curved Lie algebras

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Koszul duality and homotopy theory of curved Lie algebras. / Maunder, James.
In: Homology, Homotopy and Applications, Vol. 19, No. 1, 06.06.2017, p. 319-340.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Maunder, J 2017, 'Koszul duality and homotopy theory of curved Lie algebras', Homology, Homotopy and Applications, vol. 19, no. 1, pp. 319-340. https://doi.org/10.4310/HHA.2017.v19.n1.a16

APA

Maunder, J. (2017). Koszul duality and homotopy theory of curved Lie algebras. Homology, Homotopy and Applications, 19(1), 319-340. https://doi.org/10.4310/HHA.2017.v19.n1.a16

Vancouver

Maunder J. Koszul duality and homotopy theory of curved Lie algebras. Homology, Homotopy and Applications. 2017 Jun 6;19(1):319-340. doi: 10.4310/HHA.2017.v19.n1.a16

Author

Maunder, James. / Koszul duality and homotopy theory of curved Lie algebras. In: Homology, Homotopy and Applications. 2017 ; Vol. 19, No. 1. pp. 319-340.

Bibtex

@article{9b01a311f3bc479d8b5ffa5042f01e3e,
title = "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.",
keywords = "curved Lie algebra, homotopy, Koszul duality, deformation functor",
author = "James Maunder",
year = "2017",
month = jun,
day = "6",
doi = "10.4310/HHA.2017.v19.n1.a16",
language = "English",
volume = "19",
pages = "319--340",
journal = "Homology, Homotopy and Applications",
issn = "1532-0073",
publisher = "International Press of Boston, Inc.",
number = "1",

}

RIS

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 -