Locally compact contractive local groups

Lou van den Dries, Isaac Goldbring

Research output: Contribution to journalArticle

Abstract

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.

Original languageEnglish (US)
Pages (from-to)685-695
Number of pages11
JournalJournal of Lie Theory
Volume19
Issue number4
StatePublished - 2009

Fingerprint

Locally Compact
Locally Connected
Structure Theorem
Automorphism
Isomorphic
Analogue
Theorem

Keywords

  • Contractive pseudoautomorphisms
  • Locally compact local groups
  • Mal'cev's theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Locally compact contractive local groups. / van den Dries, Lou; Goldbring, Isaac.

In: Journal of Lie Theory, Vol. 19, No. 4, 2009, p. 685-695.

Research output: Contribution to journalArticle

van den Dries, L & Goldbring, I 2009, 'Locally compact contractive local groups', Journal of Lie Theory, vol. 19, no. 4, pp. 685-695.
van den Dries, Lou ; Goldbring, Isaac. / Locally compact contractive local groups. In: Journal of Lie Theory. 2009 ; Vol. 19, No. 4. pp. 685-695.
@article{7d7cdfe840d54f96be56407dfa32e67c,
title = "Locally compact contractive local groups",
abstract = "We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.",
keywords = "Contractive pseudoautomorphisms, Locally compact local groups, Mal'cev's theorem",
author = "{van den Dries}, Lou and Isaac Goldbring",
year = "2009",
language = "English (US)",
volume = "19",
pages = "685--695",
journal = "Journal of Lie Theory",
issn = "0949-5932",
publisher = "Heldermann Verlag",
number = "4",

}

TY - JOUR

T1 - Locally compact contractive local groups

AU - van den Dries, Lou

AU - Goldbring, Isaac

PY - 2009

Y1 - 2009

N2 - We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.

AB - We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.

KW - Contractive pseudoautomorphisms

KW - Locally compact local groups

KW - Mal'cev's theorem

UR - http://www.scopus.com/inward/record.url?scp=77949411115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949411115&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77949411115

VL - 19

SP - 685

EP - 695

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 4

ER -