The geometric classification of nilpotent Tortkara algebras

DOI10.1080/00927872.2019.1635612OpenAlexW3098832712MaRDI QIDQ5216216

Ilya B. Gorshkov, Mykola Khrypchenko, I. B. Kaĭgorodov

Publication date: 17 February 2020

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

Full work available at URL: https://arxiv.org/abs/1906.02189

zbMATH Keywords

Lie algebradegenerationnilpotent algebraMalcev algebrageometric classificationTortkara algebra

Mathematics Subject Classification ID

Nonassociative algebras satisfying other identities (17A30) Mal'tsev rings and algebras (17D10)

Related Items

The algebraic classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic and geometric classification of nilpotent bicommutative algebras ⋮ Central extensions of filiform Zinbiel algebras ⋮ Central extensions of 3-dimensional Zinbiel algebras ⋮ The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four ⋮ 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 anticommutative algebras ⋮ The geometric classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic and geometric classification of nilpotent noncommutative Jordan algebras ⋮ The algebraic and geometric classification of nilpotent assosymmetric algebras ⋮ Degenerations of nilpotent associative commutative algebras ⋮ The algebraic and geometric classification of nilpotent right alternative algebras ⋮ The algebraic classification of nilpotent commutative CD-algebras

Cites Work

• The algebraic and geometric classification of nilpotent bicommutative algebras
• Varieties of nilpotent Lie algebras of dimension less than six
• A characterization of orbit closure and applications
• Classification of orbit closures of 4-dimensional complex Lie algebras
• The variety of 7-dimensional 2-step nilpotent Lie algebras
• Nilpotency of Zinbiel algebras
• \(p\)-filiform Zinbiel algebras
• The algebraic and geometric classification of nilpotent assosymmetric algebras
• Degenerations of nilpotent algebras
• Degenerations of Jordan superalgebras
• When the group ring of a finite simple group is serial
• The algebraic and geometric classification of nilpotent Novikov algebras
• Naturally graded Zinbiel algebras with nilindex \(n-3\)
• Deformation of Dual Leibniz Algebra Morphisms
• Degenerations of 6-dimensional nilpotent lie algebras over C
• ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS
• Degenerations of pre-Lie algebras
• Identities of dual Leibniz algebras
• On Rigid 2-Step Nilpotent Lie Algebras
• The geometric classification of Leibniz algebras
• On tortkara triple systems
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Degenerations of binary Lie and nilpotent Malcev algebras
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• Complete classification of algebras of level two
• The algebraic classification of nilpotent Tortkara algebras
• On degenerations of Lie superalgebras
• The classification of 2-dimensional rigid algebras
• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
• The algebraic and geometric classification of nilpotent binary Lie algebras
• Degenerations of Leibniz and Anticommutative Algebras
• CLASSIFICATION OF ORBIT CLOSURES IN THE VARIETY OF THREE-DIMENSIONAL NOVIKOV ALGEBRAS
• The Variety of Nilpotent Tortkara Algebras