Displaying similar documents to “Lie algebras all of whose subalgebras are supersolvable.”

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.

The existence of c-covers of Lie algebras

Mohammad Reza Rismanchian (2015)

Colloquium Mathematicae

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The aim of this work is to obtain the structure of c-covers of c-capable Lie algebras. We also obtain some results on the existence of c-covers and, under some assumptions, we prove the absence of c-covers of Lie algebras.

Some examples of nil Lie algebras

Ivan P. Shestakov, Efim Zelmanov (2008)

Journal of the European Mathematical Society

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Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.

Spectrum for a solvable Lie algebra of operators

Daniel Beltiţă (1999)

Studia Mathematica

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A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.