Transitivity of inner automorphisms in infinite dimensional Cartan factors
|Title:||Transitivity of inner automorphisms in infinite dimensional Cartan factors||Authors:||Hügli, Remo V.
|Permanent link:||http://hdl.handle.net/10197/7057||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 algebra; Cartan-factors||DOI:||10.1007/s00209-008-0366-x||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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