On Classification of Filiform Leibniz Algebras

DOI10.1142/S1005386715000668zbMath1356.17002OpenAlexW2243740128WikidataQ123149763 ScholiaQ123149763MaRDI QIDQ3460283

J. R. Gómez, Bakhrom A. Omirov

Publication date: 7 January 2016

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1005386715000668

zbMATH Keywords

Lie algebraLeibniz algebranatural gradationadapted basisfiliform Leibniz algebra

Mathematics Subject Classification ID

Solvable, nilpotent (super)algebras (17B30) Leibniz algebras (17A32) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36)

Related Items (12)

Central extensions of 2-filiform Leibniz algebras ⋮ Classification of \(p\)-adic 6-dimensional filiform Leibniz algebras by solutions of \(x^q=a\) ⋮ Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras ⋮ Some irreducible components of the variety of complex \((n + 1)\)-dimensional Leibniz algebras ⋮ On isomorphism criterion for a subclass of complex filiform Leibniz algebras ⋮ Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras ⋮ On the dimension of the Schur \(\mathsf{Lie}\)-multiplier of a pair of Leibniz algebras ⋮ Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras ⋮ \(n\)-dimensional filiform Leibniz algebras of length \((n-1)\) and their derivations ⋮ Classification of naturally graded Zinbiel algebras with characteristic sequence equal to \((n-p, p)\) ⋮ Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type ℒ¹ and ℒ³ ⋮ Right and left solvable extensions of an associative Leibniz algebra

Cites Work

• Conjugacy of Cartan subalgebras of complex finite-dimensional Leibniz algebras
• Naturally graded quasi-filiform Leibniz algebras
• Leibniz homology of dialgebras of matrices
• Low-dimensional filiform Lie algebras
• Universal enveloping algebras of Leibniz algebras and (co)homology
• Complex filiform Lie algebras of dimension 11.
• A new method for classifying complex filiform Lie algebras
• Some Theorems on Leibniz Algebras
• Versal Deformations of Leibniz Algebras
• ON LIE-LIKE COMPLEX FILIFORM LEIBNIZ ALGEBRAS
• Non-abelian Tensor Product of Leibniz Algebras and an Exact Sequence in Leibniz Homology

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