Displaying similar documents to “Dipolarizations in semisimple Lie algebras and homogeneous parakähler manifolds.”

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

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We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

Remarks on local Lie algebras of pairs of functions

Josef Janyška (2018)

Czechoslovak Mathematical Journal

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Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.

Family algebras.

Kirillov, A.A. (2000)

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

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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.

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.

Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform

Detlev Poguntke (2010)

Colloquium Mathematicae

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For any connected Lie group G and any Laplacian Λ = X²₁ + ⋯ + X²ₙ ∈ 𝔘𝔤 (X₁,...,Xₙ being a basis of 𝔤) one can define the commutant 𝔅 = 𝔅(Λ) of Λ in the convolution algebra ℒ¹(G) as well as the commutant ℭ(Λ) in the group C*-algebra C*(G). Both are involutive Banach algebras. We study these algebras in the case of a "distinguished Laplacian" on the "Iwasawa part AN" of a semisimple Lie group. One obtains a fairly good description of these algebras by objects derived from the semisimple...

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]).

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...

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.