English

20 Pages

Gain access to the library to view online

__
Learn more
__

Description

Niveau: Supérieur, Doctorat, Bac+8

Chapter 11 Buildings and Kac-Moody Groups Bertrand Remy Universite de Lyon, CNRS; Universite Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France, Abstract. This survey paper provides an overview of some aspects of the theory buildings in connection with geometric and analytic group theory. Keywords: Buildings, Geometric and analytic group theory, Kac-Moody groups Subject Classifications: AMS classification (2000): 20E42, 51E24, 20F32, 20F67, 20F69, 22F, 22F10, 22F50 1 Introduction 1. The general goal of this survey paper is to introduce a class of metric spaces with remarkable symmetry properties (buildings), and a class of finitely gener- ated groups acting on some of them (Kac-Moody groups). Then – and mostly – we mention what the viewpoint of geometric group theory enabled one to prove in the very recent years. More precisely, we deal with the following topics – see the structure of the paper at the end of the introduction to find the exact places. – Simplicity: Kac-Moody groups provide a wide class of infinite finitely gener- ated, often finitely presented and Kazhdan, simple groups (Caprace–Remy). – Rigidity: these groups enjoy strong rigidity properties, e.

Chapter 11 Buildings and Kac-Moody Groups Bertrand Remy Universite de Lyon, CNRS; Universite Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France, Abstract. This survey paper provides an overview of some aspects of the theory buildings in connection with geometric and analytic group theory. Keywords: Buildings, Geometric and analytic group theory, Kac-Moody groups Subject Classifications: AMS classification (2000): 20E42, 51E24, 20F32, 20F67, 20F69, 22F, 22F10, 22F50 1 Introduction 1. The general goal of this survey paper is to introduce a class of metric spaces with remarkable symmetry properties (buildings), and a class of finitely gener- ated groups acting on some of them (Kac-Moody groups). Then – and mostly – we mention what the viewpoint of geometric group theory enabled one to prove in the very recent years. More precisely, we deal with the following topics – see the structure of the paper at the end of the introduction to find the exact places. – Simplicity: Kac-Moody groups provide a wide class of infinite finitely gener- ated, often finitely presented and Kazhdan, simple groups (Caprace–Remy). – Rigidity: these groups enjoy strong rigidity properties, e.

- group
- compact subgroup
- kac-moody groups
- groups cannot
- property
- subgroups ?
- locally finite
- arbi- trary locally compact

Subjects

Informations

Published by | mijec |

Published | 01 November 1918 |

Reads | 84 |

Language | English |

Report a problem