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Register a new userSolvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals
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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.
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In this paper solvable Leibniz algebras with naturally graded non-Lie $p$-filiform $(n-pgeq4)$ nilradical and with one-dimensional complemented space of nilradical are described. Moreover, solvable Leibniz algebras with abelian nilradical and extremal (minimal, maximal) dimensions of complemented space nilradical are studied. The rigidity of solvable Leibniz algebras with abelian nilradical and maximal dimension of its complemented space is proved.
We describe solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length.
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}.
In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.
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