Abstract

GUTIERREZ GARCIA, ISMAEL  and  NAVARRO GUTIERREZ, MANUEL. Classes of Lie's algebras and Cartan's subalgebras. Rev.colomb.mat. [online]. 2008, vol.42, n.1, pp.47-60. ISSN 0034-7426.

In this work we will consider the extension of the classical arguments on the existence and conjugation of the Cartan subalgebras of a soluble Lie algebra. Also, a change in the classical terminology is presented taking into account the base of the modern presentation of the finite soluble groups classes. Finally we proof that the N-projectors of a finite dimensional soluble Lie algebra coincide with its Cartan subalgebras, where N is the class of all the nilpotentes Lie algebra.

Keywords : Soluble and nilpotent Lie Algebras; Cartan subalgebras; classes of soluble Lie algebrasand N-proyectores.

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