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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 839-842 (août 2010)
Doi : 10.1016/j.crma.2010.07.012
Received : 3 June 2010 ;  accepted : 12 July 2010
Steinberg groups for Jordan pairs
Groupes de Steinberg pour les paires de Jordan
 

Ottmar Loos a , Erhard Neher b
a Fakultät für Mathematik und Informatik, FernUniversität in Hagen, 58097 Hagen, Germany 
b Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada 

Abstract

We announce results on projective elementary groups and on Steinberg groups associated to Jordan pairs V with a grading by a locally finite 3-graded root system Φ : The projective elementary group   of V is a group with Φ -commutator relations with respect to appropriately defined root subgroups. Under some mild additional conditions, the Steinberg group associated to   uniquely covers all central extensions of   and is the universal central extension of   if Φ is irreducible and has infinite rank.

The full text of this article is available in PDF format.
Résumé

Nous annonçons les résultats suivants relatifs aux groupes élémentaires projectifs et aux groupes de Steinberg associés aux paires de Jordan V munies d'une graduation par un système de racines Φ localement fini : Le groupe élémentaire projectif   est un groupe avec des relations de commutateurs de type Φ par rapport à certains sous-groupes radiciels. Sous des conditions additionnelles faibles, le groupe de Steinberg associé à   couvre de manière unique chaque extension centrale de   et il est l'extension centrale universelle de   si Φ est irréductible et de rang infini.

The full text of this article is available in PDF format.


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