Tori invariant under an involutorial automorphism. I
type: Item
instance of: scholarly article
title: Tori invariant under an involutorial automorphism. I
zbMATH Open document ID: 0731.20029
DOI: 10.1016/0001-8708(91)90048-C
published in: Advances in Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Sei G eine zusammenhängende reduktive lineare algebraische Gruppe über einem Körper k einer Charakteristik \(\neq 2\), \(\vartheta\in Aut(G)\) ein involutiver k-Automorphismus von G und \(K=G_{\vartheta}=\{g\in G\); \(\vartheta (g)=g\}\) die Menge der Fixpunkte von \(\vartheta\). Bezeichne \(G_ k\) die Menge der k-rationalen Punkte von G. In der vorliegenden Arbeit werden die \(K^ o\)-Konjugationsklassen \(\vartheta\)-stabiler maximaler Tori von G klassifiziert. Dies ist der Beginn einer Reihe von Veröffentlichungen, die zu einer Klassifikation aller Bahnen affiner symmetrischer Räume unter Aktion einer minimalen parabolischen Untergruppe führen sollen. Für \(k={\mathbb{R}}\) ergibt sich eine Korrespondenz mit den Konjugationsklassen von Cartan-Unteralgebren einer reellen halbeinfachen Liealgebra und dies führt zu Verallgemeinerungen von Resultaten von Kostant, Sugiura und Schmid.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 4208381
zbMATH Keywords: connected reductive linear algebraic group
zbMATH Keywords: involutional k-automorphism
zbMATH Keywords: set of fixed points
zbMATH Keywords: rational points
zbMATH Keywords: conjugacy classes of maximal tori
zbMATH Keywords: Cartan subalgebras of real semisimple Lie algebra
zbMATH Keywords: orbits of affine symmetric spaces
author: Aloysius G. Helminck
reviewed by: Heinrich Reitberger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208381