Displaying similar documents to “Almost alternative algebras”

Enveloping algebras of Malcev algebras

Murray R. Bremner, Irvin R. Hentzel, Luiz A. Peresi, Marina V. Tvalavadze, Hamid Usefi (2010)

Commentationes Mathematicae Universitatis Carolinae

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We first discuss the construction by Pérez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple...

An overview of free nilpotent Lie algebras

Pilar Benito, Daniel de-la-Concepción (2014)

Commentationes Mathematicae Universitatis Carolinae

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Any nilpotent Lie algebra is a quotient of a free nilpotent Lie algebra of the same nilindex and type. In this paper we review some nice features of the class of free nilpotent Lie algebras. We will focus on the survey of Lie algebras of derivations and groups of automorphisms of this class of algebras. Three research projects on nilpotent Lie algebras will be mentioned.

Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.

Sergio A. Albeverio, Ayupov, Shavkat, A. 2, Bakhrom A. Omirov (2006)

Revista Matemática Complutense

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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.