Degenerations of nilpotent algebras

DOI10.1016/j.jpaa.2021.106850zbMath1486.17001arXiv1905.05361OpenAlexW3197166864MaRDI QIDQ2229969

Amir Fernández Ouaridi, Yury Volkov, Mykola Khrypchenko, I. B. Kaĭgorodov

Publication date: 17 September 2021

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05361

zbMATH Keywords

nilpotent algebracommutative algebraalgebraic classificationgeometric classificationanticommutative algebracentral extension, degeneration.

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Fibrations, degenerations in algebraic geometry (14D06) Solvable, nilpotent (super)algebras (17B30) Nonassociative algebras satisfying other identities (17A30) Other nonassociative rings and algebras (17D99)

Related Items (24)

The algebraic classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic classification of nilpotent algebras ⋮ The algebraic and geometric classification of Zinbiel 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 ⋮ Central extensions of 3-dimensional Zinbiel algebras ⋮ The algebraic and geometric classification of transposed Poisson algebras ⋮ The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four ⋮ Transposed Poisson structures ⋮ Degenerations of noncommutative Heisenberg algebras ⋮ The geometric classification of nilpotent algebras ⋮ Non-degenerate evolution algebras ⋮ The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras ⋮ The algebraic and geometric classification of nilpotent anticommutative algebras ⋮ The algebraic and geometric classification of nilpotent noncommutative Jordan algebras ⋮ The algebraic and geometric classification of nilpotent terminal algebras ⋮ The geometric classification of nilpotent Tortkara algebras ⋮ Degenerations of nilpotent associative commutative algebras ⋮ The algebraic classification of nilpotent commutative algebras ⋮ The classification of nilpotent Lie-Yamaguti algebras ⋮ The algebraic classification and degenerations of nilpotent Poisson algebras ⋮ The algebraic and geometric classification of antiassociative algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classification of five-dimensional nilpotent Jordan algebras
• The classification of \(n\)-dimensional non-Lie Malcev algebras with \((n-4)\)-dimensional annihilator
• Six-dimensional nilpotent Lie algebras
• The classification of 5-dimensional \(p\)-nilpotent restricted Lie algebras over perfect fields. I.
• The algebraic and geometric classification of nilpotent bicommutative algebras
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• The classification of algebras of level two
• Varieties of nilpotent Lie algebras of dimension less than six
• A characterization of orbit closure and applications
• The algebraic and geometric classification of associative algebras of dimension five
• Classifying generic algebras
• On the level of some solvable Lie algebras
• Classification of orbit closures of 4-dimensional complex Lie algebras
• Classification of nilpotent Malcev algebras of small dimensions over arbitrary fields of characteristic not 2
• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent assosymmetric algebras
• Non-associative central extensions of null-filiform associative algebras
• Degenerations of Jordan superalgebras
• Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
• On classification of four-dimensional nilpotent Leibniz algebras
• Contractions of Low-Dimensional Nilpotent Jordan Algebras
• Degenerations of 6-dimensional nilpotent lie algebras over C
• Degenerations of pre-Lie algebras
• The geometric classification of Leibniz algebras
• Classification of nilpotent associative algebras of small dimension
• The classification of n-dimensional anticommutative algebras with (n − 3)-dimensional annihilator
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• The classification of N-dimensional non-associative Jordan algebras with (N − 3)-dimensional annihilator
• Degenerations of Filippov algebras
• Complete classification of algebras of level two
• The algebraic classification of nilpotent Tortkara algebras
• On geometric degenerations and Gerstenhaber formal deformations
• On degenerations of Lie superalgebras
• The geometric classification of nilpotent Tortkara algebras
• 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
• Central extensions of filiform associative algebras

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