The classification of 4-dimensional Leibniz algebras

DOI10.1016/j.laa.2013.02.035zbMath1332.17005arXiv1301.7665OpenAlexW2155918884WikidataQ122893918 ScholiaQ122893918MaRDI QIDQ389620

Elisa M. Cañete, A. Kh. Khudoyberdiyev

Publication date: 21 January 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7665

zbMATH Keywords

Lie algebrasLeibniz algebrasderivationsolvable Leibniz algebras

Mathematics Subject Classification ID

Leibniz algebras (17A32) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36)

Related Items (49)

Arbitrary algebras with a multiplicative basis ⋮ Classification of some solvable Leibniz algebras ⋮ The classification of \(n\)-dimensional non-Lie Malcev algebras with \((n-4)\)-dimensional annihilator ⋮ Algorithmic procedure to compute abelian subalgebras and ideals of maximal dimension of Leibniz algebras ⋮ Itô’s theorem and metabelian Leibniz algebras ⋮ Description of solvable Leibniz algebras with four-dimensional nilradical ⋮ On classification problem of Loday algebras ⋮ One-generated nilpotent Novikov algebras ⋮ The Schur Lie-multiplier of Leibniz algebras ⋮ On metric Leibniz algebras and deformations ⋮ The geometric classification of Leibniz algebras ⋮ The global extension problem, co-flag and metabelian Leibniz algebras ⋮ On some classes of solvable Leibniz algebras and their completeness ⋮ Unnamed Item ⋮ Leibniz algebras associated with representations of filiform Lie algebras ⋮ The algebraic and geometric classification of nilpotent Novikov algebras ⋮ Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras ⋮ Rota-Baxter Leibniz algebras and their constructions ⋮ The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras ⋮ Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras ⋮ Modules over linear spaces admitting a multiplicative basis ⋮ Classification of nilpotent Malcev algebras of small dimensions over arbitrary fields of characteristic not 2 ⋮ Second-maximal subalgebras of Leibniz algebras ⋮ Leibniz algebras with small derived ideal ⋮ Classification of solvable Leibniz algebras with abelian nilradical and (k−1)-dimensional extension ⋮ Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals ⋮ Unified products for Leibniz algebras. Applications ⋮ Unnamed Item ⋮ On classification of four-dimensional nilpotent Leibniz algebras ⋮ Solvable Leibniz algebras with triangular nilradicals ⋮ On Lie-central extensions of Leibniz algebras ⋮ The algebraic and geometric classification of nilpotent noncommutative Jordan algebras ⋮ Leibniz algebras admitting a multiplicative basis ⋮ On classification of 5-dimensional solvable Leibniz algebras ⋮ Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second typeℒ² ⋮ The algebraic and geometric classification of nilpotent left-symmetric algebras ⋮ A study of n-Lie-isoclinic Leibniz algebras ⋮ Residually solvable extensions of an infinite dimensional filiform Leibniz algebra ⋮ Leibniz triple systems admitting a multiplicative basis ⋮ \textsf{Lie}-isoclinism of pairs of Leibniz algebras ⋮ The algebraic classification of nilpotent commutative algebras ⋮ The Variety of Two-dimensional Algebras Over an Algebraically Closed Field ⋮ Solvable Leibniz algebras with naturally graded non-Liep-filiform nilradicals ⋮ Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type ℒ¹ and ℒ³ ⋮ Leibniz algebras as non-associative algebras ⋮ Classification of (2n−1)-dimensional solvable Leibniz algebras with n-dimensional nilradical ⋮ A note on outer derivations of Leibniz algebras ⋮ Solvable Leibniz Algebras with Heisenberg Nilradical ⋮ Right and left solvable extensions of an associative Leibniz algebra

Cites Work

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• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
• On Engel's Theorem for Leibniz Algebras
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• Solvable Lie algebras with an \mathbb {N}-graded nilradical of maximal nilpotency degree and their invariants
• A class of solvable Lie algebras and their Casimir invariants
• ON NILPOTENT AND SIMPLE LEIBNIZ ALGEBRAS
• Solvable Lie algebras with Abelian nilradicals
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• Solvable Lie algebras with triangular nilradicals
• Classification of solvable Leibniz algebras with null-filiform nilradical

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