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Register a new userSolvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length
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We describe solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length.
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The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the nilradical has maximal dimension, are described up to isomorphism.
In this paper solvable Leibniz algebras whose nilradical is quasi-filiform Lie algebra of maximum length, are classified. The rigidity of such Leibniz algebras with two-dimensional complemented space to nilradical is proved.
In this paper we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals, and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra, as well.
The descriptions (up to isomorphism) of naturally graded $p$-filiform Leibniz algebras and $p$-filiform ($pleq 3$) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for $p$-filiform Leibniz algebras. The present work aims at the classification of complex $p$-filiform ($p geq 4$) Leibniz algebras of maximum length.
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classification of the $3$-filiform Leibniz algebras of maximum length cite{3-filiform}. Moreover, due to the good structure of the algebras of maximum length, we also tackle some of their cohomological properties. Our main tools are the previous result of Cabezas and Pastor cite{Pastor}, the construction of appropriate homogeneous basis in the considered connected gradation and the computational support provided by the two programs implemented in the software textit{Mathematica}.
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