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Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

100%
Ladra M., Omirov B., Rozikov U.
Open Mathematics
|
2013
|
tom 11
|
nr 6
1083-1093
EN
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.
2
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The Leibniz algebras whose subalgebras are ideals

76%
Kurdachenko L. A., Semko N. N., Subbotin I. Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
92-100
EN
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
3
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Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical

76%
Camacho L. M., Omirov B. A., Masutova K. K., Rikhsiboev I. M.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1371-1388
EN
All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.
4
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Left-right noncommutative Poisson algebras

64%
Casas J., Datuashvili T., Ladra M.
Open Mathematics
|
2014
|
tom 12
|
nr 1
57-78
EN
The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as special cases of the corresponding wellknown notions in categories of groups with operations. The cohomologies of NPlr-algebras and AWBlr (resp. of NPr-algebras and AWBr) are defined and the relations between them and the Hochschild, Quillen and Leibniz cohomologies are detected. The cases P is a free AWBr, the Hochschild or/and Leibniz cohomological dimension of P is ≤ n are considered separately, exhibiting interesting possibilities of representations of the new cohomologies by the well-known ones and relations between the corresponding cohomological dimensions.
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