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

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.

On a nilpotent Lie superalgebra which generalizes Q.

José María Ancochea Bermúdez, Otto Rutwig Campoamor (2002)

Revista Matemática Complutense

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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

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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.

On the q-exponential of matrix q-Lie algebras

Thomas Ernst (2017)

Special Matrices

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In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with...