The algebraic and geometric classification of nilpotent bicommutative algebras

DOI10.1007/s10468-019-09944-xzbMath1487.17003arXiv1903.08997OpenAlexW3096845759MaRDI QIDQ829542

Pilar Páez-Guillán, Vasily Voronin, I. B. Kaĭgorodov

Publication date: 6 May 2021

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.08997

zbMATH Keywords

degenerationnilpotent algebrascentral extensionalgebraic classificationgeometric classificationbicommutative algebras

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Fibrations, degenerations in algebraic geometry (14D06) Nonassociative algebras satisfying other identities (17A30)

Related Items (27)

The algebraic classification of nilpotent ℭ𝔇-algebras ⋮ The algebraic classification of nilpotent algebras ⋮ One-generated nilpotent Novikov algebras ⋮ One-generated nilpotent assosymmetric algebras ⋮ Central extensions of filiform Zinbiel algebras ⋮ Gelfand-Kirillov dimension of bicommutative algebras ⋮ Central extensions of 3-dimensional Zinbiel algebras ⋮ Non-associative central extensions of null-filiform associative algebras ⋮ Degenerations of Filippov algebras ⋮ The geometric classification of nilpotent algebras ⋮ Invariant theory of free bicommutative algebras ⋮ The algebraic classification of nilpotent Tortkara algebras ⋮ One-generated nilpotent terminal algebras ⋮ Degenerations of nilpotent algebras ⋮ Degenerations of 8-dimensional 2-step nilpotent Lie 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 right commutative algebras ⋮ The geometric classification of nilpotent Tortkara algebras ⋮ Degenerations of nilpotent associative commutative algebras ⋮ The algebraic and geometric classification of nilpotent binary Lie algebras ⋮ The algebraic and geometric classification of nilpotent right alternative algebras ⋮ The algebraic classification of nilpotent commutative CD-algebras ⋮ The algebraic classification and degenerations of nilpotent Poisson algebras

Cites Work

• 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.
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• 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
• Classification of nilpotent Malcev algebras of small dimensions over arbitrary fields of characteristic not 2
• Noetherianity and Specht problem for varieties of bicommutative algebras
• The algebraic and geometric classification of nilpotent anticommutative 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 the degenerations of solvable Leibniz algebras
• On classification of four-dimensional nilpotent Leibniz algebras
• Erratum and addendum to ‘‘Central extensions of current algebras”
• Complete LR-structures on solvable Lie algebras
• LR-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
• Polynomial identities of bicommutative algebras, Lie and Jordan elements
• 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 binary Lie and nilpotent Malcev algebras
• Bicommutative algebras
• Degenerations of Filippov algebras
• Complete classification of algebras of level two
• The algebraic classification of nilpotent Tortkara algebras
• Rota-type operators on null-filiform associative algebras
• The geometric classification of nilpotent Tortkara algebras
• The classification of 2-dimensional rigid algebras
• Degenerations of nilpotent associative commutative 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

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