Displaying similar documents to “The Lie ring associated with certain groups”

Lie commutators in a free diassociative algebra

A.S. Dzhumadil'daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

Similarity:

We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.

An overview of free nilpotent Lie algebras

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

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

On a nilpotent Lie superalgebra which generalizes Q.

José María Ancochea Bermúdez, Otto Rutwig Campoamor (2002)

Revista Matemática Complutense

Similarity:

In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra L are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Q, which only exists in even dimension as a consequence of the centralizer property....

The dynamic of a Lie group endomorphism

Víctor Ayala, Heriberto Román-Flores, Adriano Da Silva (2017)

Open Mathematics

Similarity:

For a given endomorphism φ on a connected Lie group G this paper studies several subgroups of G that are intrinsically connected with the dynamic behavior of φ.