Solvable Leibniz algebras with NFn⊕ Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical
L.M. CamachoDpto. Matemática Aplicada I. Universidad de Sevilla. Avda. Reina Mercedes, s/n. 41012 Sevilla, SpainB. A. OmirovInstitute of Mathematics. National University of Uzbekistan, 29, Do’rmon yo’li street., 100125, Tashkent, UzbekistanK. K. MasutovaInstitute of Mathematics. National University of Uzbekistan, 29, Do’rmon yo’li street., 100125, Tashkent, UzbekistanI. M. RikhsiboevUniversiti Kuala Lumpur, Malaysian Institute of Industrial Technology, Bandar Seri Alam, 81750 Johor Bahru, Malaysia
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Аннотация
Abstract All finite-dimensional solvable Leibniz algebras L , having N = NF n ⊕ $\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. NF n and $\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.
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