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We consider the classification problem for special classes of nilpotent Leibniz algebras. Namely, we consider “naturally” graded nilpotent n-dimensional Leibniz algebras for which the right multiplication operator (by the generic element) has two Jordan blocks of dimensionsm and n ? m. Earlier, the problem of classifying such algebras was studied form < 4. The present paper continues these studies for the case m ≥ 4. 相似文献
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L. M. Camacho E. M. Cañete J. R. Gómez B. A. Omirov 《Siberian Mathematical Journal》2011,52(5):840-853
The n-dimensional p-filiform Leibniz algebras of maximum length have already been studied with 0 ≤ p ≤ 2. For Lie algebras whose nilindex is equal to n−2 there is only one characteristic sequence, (n − 2, 1, 1), while in Leibniz theory we obtain the two possibilities: (n − 2, 1, 1) and (n − 2, 2). The first case (the 2-filiform case) is already known. The present paper deals with the second case, i.e., quasi-filiform
non-Lie-Leibniz algebras of maximum length. Therefore this work completes the study of the maximum length of the Leibniz algebras
with nilindex n − p with 0 ≤ p ≤ 2. 相似文献
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B. A. Omirov 《Mathematical Notes》2005,77(5-6):677-685
The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov. 相似文献
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Manuel Ladra Bakhrom A. Omirov Utkir A. Rozikov 《Central European Journal of Mathematics》2013,11(6):1083-1093
We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p ? 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras. 相似文献
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Alice Fialowski A. Kh. Khudoyberdiyev B. A. Omirov 《Algebras and Representation Theory》2013,16(5):1489-1505
W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper, using the definition of a Leibniz-derivation from Moens (2010), we show that a similar result for non-Lie Leibniz algebras is not true. Namely, we give an example of non-nilpotent Leibniz algebra that admits an invertible Leibniz-derivation. In order to extend the results of the paper by Moens (2010) for Leibniz algebras, we introduce a definition of a Leibniz-derivation of Leibniz algebras that agrees with Leibniz-derivation of the Lie algebra case. Further, we prove that a Leibniz algebra is nilpotent if and only if it admits an invertible Leibniz-derivation of Definition 3.4. Moreover, the result that a solvable radical of a Lie algebra is invariant with respect to a Leibniz-derivation was extended to the case of Leibniz algebras. 相似文献
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ABSTRACTWe describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself. 相似文献
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L.M. Camacho J.R. Gómez B.A. Omirov R.M. Turdibaev 《Linear and Multilinear Algebra》2013,61(3):309-322
In this work, we investigate the derivations of n-dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank n ? 1 are described. 相似文献
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Bakhrom Yavidov 《Physica B: Condensed Matter》2009,404(20):3756-3760
In this work renormalization of the effective mass of an electron due to a small polaron formation is studied within the framework of the extended Holstein model. It is assumed that an electron moves along the one-dimensional chain of ions and interacts with ions vibrations of a neighboring chain via a long-range density-displacement type force. By means of the exact calculations a renormalized mass of a nonadiabatic small polaron is obtained at strong coupling limit. The obtained results compared with the mass of small polaron of ordinary Holstein model. The effect of ions vibrations polarization on the small polaron mass is addressed. 相似文献