Transitivity of inner automorphisms in infinite dimensional Cartan factors

Files in This Item:
File Description SizeFormat 
Transit-Cartan-3-3c.pdf241.89 kBAdobe PDFDownload
Title: Transitivity of inner automorphisms in infinite dimensional Cartan factors
Authors: Hügli, Remo V.
Mackey, Michael
Permanent link:
Date: May-2009
Online since: 2015-09-17T14:57:57Z
Abstract: Let C be a Cartan-factor having arbitrary dimension dimC. It is shown that the group Inn(C) of inner automorphisms of C acts transitively on the manifold Ur(C) of tripotents with finite rank r in C. This extends results by Loos (Bounded Symmetric Domains and Jordan Pairs. Mathematical Lectures. University of California, Irvine, 1977) valid in finite dimensions, and similar findings by Isidro et al. (Math Z 233(4):741–754, 2000; Acta Sci Math (Szeged) 66(3–4), 2000; Expo Math 20(2):97–116, 2002; Q J Math 57(4):505–525, 2006). Hence, the results presented here close a significant gap concerning the transitivity property of the general infinite-dimensional case. The proofs given here are based on new methods, independent of those used for the finite-dimensional cases.
Type of material: Journal Article
Publisher: Springer
Journal: Mathematische Zeitschrift
Volume: 262
Issue: 1
Start page: 125
End page: 141
Copyright (published version): 2008 Springer-Verlag
Keywords: Jordan operator algebraCartan-factors
DOI: 10.1007/s00209-008-0366-x
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

Citations 50

Last Week
Last month
checked on Feb 11, 2019

Google ScholarTM



This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.