The algebraic and geometric classification of nilpotent binary Lie algebras

DOI10.1142/S0218196719500437zbMath1473.17086arXiv1902.01706OpenAlexW2931793369WikidataQ115245888 ScholiaQ115245888MaRDI QIDQ5237449

Hani Abdelwahab, Antonio Jesús Calderón Martín, I. B. Kaĭgorodov

Publication date: 18 October 2019

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01706

zbMATH Keywords

degenerationLie algebrasnilpotent algebrasMalcev algebrasalgebraic classificationgeometric classificationbinary Lie algebras\(\mathfrak{CD}\)-algebras

Mathematics Subject Classification ID

Mal'tsev rings and algebras (17D10) (non-Lie) Hom algebras and topics (17D30)

Related Items (32)

The algebraic classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic and geometric classification of nilpotent bicommutative algebras ⋮ The algebraic classification of nilpotent algebras ⋮ One-generated nilpotent Novikov algebras ⋮ One-generated nilpotent assosymmetric algebras ⋮ The geometric classification of nilpotent commutative \(\mathfrak{CD}\)-algebras ⋮ Central extensions of filiform Zinbiel algebras ⋮ On anticommutative algebras for which \([R_a,R_b\) is a derivation] ⋮ Central extensions of 3-dimensional Zinbiel algebras ⋮ The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four ⋮ Non-associative central extensions of null-filiform associative algebras ⋮ The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras ⋮ The algebraic classification of nilpotent Tortkara algebras ⋮ One-generated nilpotent terminal algebras ⋮ The algebraic classification of nilpotent associative commutative algebras ⋮ The variety of dual mock-Lie algebras ⋮ Degenerations of nilpotent algebras ⋮ Degenerations of 8-dimensional 2-step nilpotent Lie algebras ⋮ The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras ⋮ The algebraic and geometric classification of nilpotent anticommutative algebras ⋮ Unified computational approach to nilpotent algebra classification problems ⋮ The geometric classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic and geometric classification of nilpotent noncommutative Jordan algebras ⋮ The algebraic and geometric classification of nilpotent terminal algebras ⋮ The algebraic and geometric classification of nilpotent assosymmetric algebras ⋮ The geometric classification of nilpotent Tortkara algebras ⋮ Degenerations of nilpotent associative commutative algebras ⋮ The algebraic and geometric classification of nilpotent right alternative algebras ⋮ The classification of nilpotent Lie-Yamaguti algebras ⋮ Classification of a family of 4-dimensional anti-commutative algebras and their automorphisms ⋮ The algebraic classification of nilpotent commutative CD-algebras ⋮ The algebraic classification and degenerations of nilpotent Poisson algebras

Cites Work

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• The classification of \(n\)-dimensional non-Lie Malcev algebras with \((n-4)\)-dimensional annihilator
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• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• A characterization of orbit closure and applications
• Lie triple algebras
• Classification of nilpotent Malcev algebras of small dimensions over arbitrary fields of characteristic not 2
• Binary Lie algebras without strong zero divisors
• Malcev Algebras
• The geometric classification of Leibniz algebras
• Classification of nilpotent associative algebras of small dimension
• On a ternary generalization of Jordan algebras
• The classification of n-dimensional anticommutative algebras with (n − 3)-dimensional annihilator
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Degenerations of binary Lie and nilpotent Malcev algebras
• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field

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