Vol. 236, No. 1, 2008

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2 × 2-symmetric spaces

Yuri Bahturin and Michel Goze

Vol. 236 (2008), No. 1, 1–21
Abstract

The notion of a Γ-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group Γ replaces the group 2. We approach the classification of Γ-symmetric space in the case Γ = 2 × 2 using recent results on the classification of complex 2 × 2-graded simple Lie algebras.

Keywords
G-grading on Lie algebras, G-symmetric spaces, classification of Z22-symmetric spaces.
Mathematical Subject Classification 2000
Primary: 53C30, 53C35
Secondary: 17B40
Milestones
Received: 4 July 2007
Revised: 8 December 2007
Accepted: 2 January 2008
Published: 1 May 2008
Authors
Yuri Bahturin
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John’s, NL, A1C5S7
Canada
Michel Goze
Université de Haute Alsace
Faculté des Sciences et Techniques
Laboratoire de Mathématiques et applications
4 rue des Frères Lumière
68093 Mulhouse
France
http://www.algebre.uha.fr/goze/