Deligne groupoid revisited

Paul Bressler; Alexander Gorokhovsky; Ryszard Nest; Boris Tsygan

Deligne groupoid revisited

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Article number	29
Pages (from-to)	1001-1016
Number of pages	16
Journal	Theory and Applications of Categories
Volume	30
State	Published - Jul 7 2015

Keywords

Groupoid
L∞-algebra
Simplicial nerve

ASJC Scopus subject areas

Mathematics (miscellaneous)

Cite this

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title = "Deligne groupoid revisited",

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].",

keywords = "Groupoid, L∞-algebra, Simplicial nerve",

author = "Paul Bressler and Alexander Gorokhovsky and Ryszard Nest and Boris Tsygan",

note = "Publisher Copyright: {\textcopyright} Paul Bressler, Alexander Gorokhovsky, Ryszard Nest.",

year = "2015",

month = jul,

day = "7",

language = "English (US)",

volume = "30",

pages = "1001--1016",

journal = "Theory and Applications of Categories",

issn = "1201-561X",

publisher = "Mount Allison University",

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T1 - Deligne groupoid revisited

AU - Bressler, Paul

AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris

N1 - Publisher Copyright: © Paul Bressler, Alexander Gorokhovsky, Ryszard Nest.

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].

KW - Groupoid

KW - L∞-algebra

KW - Simplicial nerve

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M3 - Article

AN - SCOPUS:84937440626

SN - 1201-561X

VL - 30

SP - 1001

EP - 1016

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

M1 - 29

ER -

Deligne groupoid revisited

Abstract

Keywords

ASJC Scopus subject areas

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