Central extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb[1]

  • [1] Technische Universität Darmstadt, Fachbereich Mathematik AG5, Schlossgartenstrasse 7, 64289 Darmstadt (Allemagne)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 5, page 1365-1442
  • ISSN: 0373-0956

Abstract

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The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group G by an abelian group Z whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra cocycle to correspond to a locally group cocycle.

How to cite

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Neeb, Karl-Hermann. "Central extensions of infinite-dimensional Lie groups." Annales de l’institut Fourier 52.5 (2002): 1365-1442. <http://eudml.org/doc/116014>.

@article{Neeb2002,
abstract = {The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group $G$ by an abelian group $Z$ whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra cocycle to correspond to a locally group cocycle.},
affiliation = {Technische Universität Darmstadt, Fachbereich Mathematik AG5, Schlossgartenstrasse 7, 64289 Darmstadt (Allemagne)},
author = {Neeb, Karl-Hermann},
journal = {Annales de l’institut Fourier},
keywords = {infinite-dimensional Lie group; invariant form; central extension; period map; Lie group cocycle; homotopy group; local cocycle; diffeomorphism group},
language = {eng},
number = {5},
pages = {1365-1442},
publisher = {Association des Annales de l'Institut Fourier},
title = {Central extensions of infinite-dimensional Lie groups},
url = {http://eudml.org/doc/116014},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Neeb, Karl-Hermann
TI - Central extensions of infinite-dimensional Lie groups
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 5
SP - 1365
EP - 1442
AB - The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group $G$ by an abelian group $Z$ whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra cocycle to correspond to a locally group cocycle.
LA - eng
KW - infinite-dimensional Lie group; invariant form; central extension; period map; Lie group cocycle; homotopy group; local cocycle; diffeomorphism group
UR - http://eudml.org/doc/116014
ER -

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