Full paper in PDF:
$%S. A. Albeverio, S. A. Ayupov, and B. A. Omirov, Cartan subalgebras, weight spaces, and
criterion of solvability of finite dimensional Leibniz algebras, Rev. Mat. Complut. 19 (2006),
no. 1, 183–195.
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Institut für Angewandte Mathematik Universität Bonn Wegelstr. 6 D-53115 Bonn — Germany | Institute of Mathematics Uzbekistan Academy of Science F. Hodjaev str. 29 700143, Tashkent — Uzbekistan |
In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan’s criterion of solvability is proved.
Key words: Leibniz algebra, Cartan subalgebra, weight space.
2000 Mathematics Subject Classification: 17A32, 17A60, 17B30.