Full paper in PDF:
$%S. A. Albeverio, S. A. Ayupov, and B. A. Omirov, Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras, Rev. Mat. Complut. 19 (2006), no. 1, 183195. %$

Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras
Sergio A. ALBEVERIO, Shavkat A. AYUPOV,
and Bakhrom A. OMIROV
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

Received: June 23, 2005
Accepted: November 7, 2005
ABSTRACT

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.