An algorithm for the classification of 3-dimensional complex Leibniz algebras

DOI10.1016/j.laa.2011.11.039zbMath1280.17004OpenAlexW2018346921WikidataQ122931695 ScholiaQ122931695MaRDI QIDQ417514

Manuel Avelino Insua Hermo, Manuel Ladra Gonzalez, José Manuel Casas Mirás

Publication date: 14 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.11.039

zbMATH Keywords

Gröbner basesLeibniz algebra

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Leibniz algebras (17A32) Computational methods for problems pertaining to nonassociative rings and algebras (17-08)

Related Items (35)

Classification of some solvable Leibniz algebras ⋮ Algorithmic procedure to compute abelian subalgebras and ideals of maximal dimension of Leibniz algebras ⋮ On classification problem of Loday algebras ⋮ The \(c\)-nilpotent Schur \(\mathsf{Lie}\)-multiplier for the direct sum of two Leibniz algebras ⋮ The Schur Lie-multiplier of Leibniz algebras ⋮ The global extension problem, co-flag and metabelian Leibniz algebras ⋮ On split Leibniz superalgebras ⋮ Classification of some subclasses of 6−dimensional nilpotent Leibniz algebras ⋮ Unnamed Item ⋮ Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras ⋮ Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras ⋮ On the automorphism groups for some Leibniz algebras of low dimensions ⋮ On some properties of generalized \textsf{Lie}-derivations of Leibniz algebras ⋮ Biderivations of low-dimensional Leibniz algebras ⋮ On \(\mathsf{Lie}\)-isoclinic Leibniz algebras ⋮ Classification of solvable Leibniz algebras with abelian nilradical and (k−1)-dimensional extension ⋮ Unified products for Leibniz algebras. Applications ⋮ Unnamed Item ⋮ On classification of four-dimensional nilpotent Leibniz algebras ⋮ Algorithmic method to obtain combinatorial structures associated with Leibniz algebras ⋮ On Lie-central extensions of Leibniz algebras ⋮ On classification of 5-dimensional solvable Leibniz algebras ⋮ Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second typeℒ² ⋮ A study of n-Lie-isoclinic Leibniz algebras ⋮ \textsf{Lie}-isoclinism of pairs of Leibniz algebras ⋮ Leibniz algebras: a brief review of current results ⋮ Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type ℒ¹ and ℒ³ ⋮ Unnamed Item ⋮ AN ALGORITHM FOR A CLASSIFICATION OF THREE-DIMENSIONAL LEIBNIZ ALGEBRAS OVER ARBITRARY FIELDS ⋮ Classification of 5-dimensional complex nilpotent Leibniz algebras ⋮ Degenerations of Leibniz and Anticommutative Algebras ⋮ On some properties of Lie-centroids of Leibniz algebras ⋮ Classification of (2n−1)-dimensional solvable Leibniz algebras with n-dimensional nilradical ⋮ A note on outer derivations of Leibniz algebras ⋮ Right and left solvable extensions of an associative Leibniz algebra

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Test for Leibniz \(n\)-algebra structure
• A noncommutative version of Lie algebras: Leibniz algebras
• Classification of Solvable Lie Algebras
• Algèbres de Leibnitz : définitions, propriétés
• ON NILPOTENT AND SIMPLE LEIBNIZ ALGEBRAS
• Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less than Five

This page was built for publication: An algorithm for the classification of 3-dimensional complex Leibniz algebras