Deligne groupoid revisited

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris L Tsygan

Research output: Contribution to journalArticle

Abstract

We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

Original languageEnglish (US)
Article number29
Pages (from-to)1001-1016
Number of pages16
JournalTheory and Applications of Categories
Volume30
StatePublished - Jul 7 2015

Fingerprint

Simplicial Set
Graded Lie Algebras
Groupoid
Differential Forms
Nerve
Homotopy
Vanish

Keywords

  • Groupoid
  • L∞-algebra
  • Simplicial nerve

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Bressler, P., Gorokhovsky, A., Nest, R., & Tsygan, B. L. (2015). Deligne groupoid revisited. Theory and Applications of Categories, 30, 1001-1016. [29].
Bressler, Paul ; Gorokhovsky, Alexander ; Nest, Ryszard ; Tsygan, Boris L. / Deligne groupoid revisited. In: Theory and Applications of Categories. 2015 ; Vol. 30. pp. 1001-1016.
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Bressler, P, Gorokhovsky, A, Nest, R & Tsygan, BL 2015, 'Deligne groupoid revisited', Theory and Applications of Categories, vol. 30, 29, pp. 1001-1016.

Deligne groupoid revisited. / Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris L.

In: Theory and Applications of Categories, Vol. 30, 29, 07.07.2015, p. 1001-1016.

Research output: Contribution to journalArticle

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T1 - Deligne groupoid revisited

AU - Bressler, Paul

AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris L

PY - 2015/7/7

Y1 - 2015/7/7

N2 - We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

AB - We show that for a differential graded Lie algebra g whose components vanish in degrees below −1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V. Hinich [Hinich, 1997].

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KW - L∞-algebra

KW - Simplicial nerve

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Bressler P, Gorokhovsky A, Nest R, Tsygan BL. Deligne groupoid revisited. Theory and Applications of Categories. 2015 Jul 7;30:1001-1016. 29.