On Lie gradings. III: Gradings of the real forms of classical Lie algebras
type: Item
instance of: scholarly article
title: On Lie gradings. III: Gradings of the real forms of classical Lie algebras
zbMATH Open document ID: 1017.17027
DOI: 10.1016/S0024-3795(00)00099-9
published in: Linear Algebra and its Applications
publication date: 2003-05-19T00:00:00Z
review text: The authors classify maximal Abelian subgroups of diagonalizable automorphisms (in short MAD-groups) of the real forms of the classical Lie algebras. In part II [ibid. 277, 97-125 (1998; Zbl 0939.17020)] the same was done in the complex case. MAD-groups can be used to produce fine gradings of the Lie algebra. For a simple complex Lie algebra you get all fine gradings in this way, for the real forms this remains an open question.
reviewed by: Evelyn Weimar-Woods
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 1506619
zbMATH Keywords: graded Lie algebras
zbMATH Keywords: maximal Abelian subgroups
zbMATH Keywords: diagonalizable automorphisms
zbMATH Keywords: MAD-groups
author: M. Havlíček
author: Jiří Patera
author: Edita Pelantová
MaRDI profile type: Publication
cites work: Grading refinements in the contractions of Lie algebras and their invariants
cites work: Q3222341
cites work: Normal forms of elements of classical real and complex Lie and Jordan algebras
cites work: Q4040931
cites work: On Lie gradings. II
cites work: Discrete and continuous graded contractions of Lie algebras and superalgebras
cites work: Discrete and continuous graded contractions of representations of Lie algebras
cites work: Q4264074
cites work: Graded contractions of the Lie algebrae(2, 1)
cites work: On Lie gradings. I
cites work: The Pauli matrices in n dimensions and finest gradings of simple Lie algebras of type A n−1
Wikidata QID: Q115340050
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description: scientific article; zbMATH DE number 1506619