On classification of metabelian Lie algebras.
Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
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Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
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Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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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.
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]).
Agaoka, Y. (1999)
Lobachevskii Journal of Mathematics
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Kirillov, A.A. (2000)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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.
Crandall, Gordon, Dodziuk, Jósef (2002)
Journal of Lie Theory
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Richter, David A. (1999)
Journal of Lie Theory
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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.
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...
S. Berman, R.V. Moody (1992)
Inventiones mathematicae
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Ciobanu, Camelia (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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W. Laskar (1977)
Recherche Coopérative sur Programme n°25
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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.
de Graaf, W.A. (2005)
Experimental Mathematics
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