Displaying similar documents to “The construction of 3-Lie 2-algebras”

Restricted and quasi-toral restricted Lie-Rinehart algebras

Bing Sun, Liangyun Chen (2015)

Open Mathematics

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In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension...

Drinfeld-Sokolov hierarchies on truncated current Lie algebras

Paolo Casati (2011)

Banach Center Publications

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In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.

On maximal subalgebras of central simple Malcev algebras.

Alberto C. Elduque Palomo (1986)

Extracta Mathematicae

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In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).

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.

Family algebras.

Kirillov, A.A. (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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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.

Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras

Youjun Tan, Senrong Xu (2022)

Czechoslovak Mathematical Journal

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We introduce the notion of quasi-trace functions on Lie algebras. As applications we study realizations of 3-dimensional and 4-dimensional 3-Lie algebras. Some comparison results on cohomologies of 3-Lie algebras and Leibniz algebras arising from quasi-trace functions are obtained.

Self-similar Lie algebras

Laurent Bartholdi (2015)

Journal of the European Mathematical Society

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We give a general definition of branched, self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk’s and Gupta–Sidki’s torsion groups are nil as well as self-similar.We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov.

Poisson-Lie groupoids and the contraction procedure

Kenny De Commer (2015)

Banach Center Publications

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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...