(Z/2Z x Z/2Z)-symmetric spaces

2006/12/04 by Yuri Bahturin, Bahturin, Yuri, Michel Goze +1 · 1 citation
Mathematics · Physics and Astronomy · #17B20 #53C30 #53C35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0612098

openalex publication_date 2006/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Z₂. The case Γ=\Z_k has also been studied, from the algebraic point of view by V.Kac \citeVK and from the point of view of the differential geometry by Ledger, Obata, Kowalski or Wolf - Gray in terms of k-symmetric spaces. In this case, a k-manifold is an homogeneous reductive space and the classification of these varieties is given by the corresponding classification of graded Lie algebras. The general notion of a Γ-symmetric space was introduced by R.Lutz. We approach the classification of such spaces in the case Γ=Z₂² using recent results on the classification of complex Z₂²-graded simple Lie algebras.

Citations

• Group Gradings on Simple Lie Algebras of Type "A"

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