Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras

Sergio A.  Albeverio; Shavkat A.  Ayupov; Bakhrom A.  Omirov

doi:10.5209/rev_REMA.2006.v19.n1.16652

Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras

Sergio A. Albeverio
Shavkat A. Ayupov
Bakhrom A. Omirov

DOI: https://doi.org/10.5209/rev_REMA.2006.v19.n1.16652

Keywords: Leibniz algebra, Cartan subalgebra, Weight space

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.

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2006-04-27

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Albeverio, S. A., Ayupov, S. A., & Omirov, B. A. (2006). Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras. Revista Matemática Complutense, 19(1), 183-195. https://doi.org/10.5209/rev_REMA.2006.v19.n1.16652

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Vol. 19 No. 1 (2006)

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