The algebraic classification of nilpotent associative commutative algebras

DOI10.1142/S0219498820502205zbMath1460.16007OpenAlexW2979906724WikidataQ114614524 ScholiaQ114614524MaRDI QIDQ5133870

Sh. K. Said Husain, Isamiddin S. Rakhimov, I. B. Kaĭgorodov

Publication date: 11 November 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498820502205

zbMATH Keywords

associative algebranilpotent algebracommutative algebracentral extensionalgebraic classification

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Extensions of associative rings by ideals (16S70)

Related Items (11)

Classification of naturally graded nilpotent associative algebras ⋮ The algebraic classification of nilpotent ℭ𝔇-algebras ⋮ One-generated nilpotent Novikov algebras ⋮ One-generated nilpotent assosymmetric algebras ⋮ Central extensions of 3-dimensional Zinbiel algebras ⋮ Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures ⋮ Nets of conics and associated Artinian algebras of length 7. Translation and update of the 1977 version by J. Emsalem and A. Iarrobino ⋮ One-generated nilpotent terminal algebras ⋮ Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies, and multicomponent Hunter-Saxton equations ⋮ The algebraic classification of nilpotent commutative algebras ⋮ The algebraic classification of nilpotent commutative CD-algebras

Cites Work

• 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.
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• The algebraic and geometric classification of associative algebras of dimension five
• Generic finite schemes and Hochschild cocycles
• 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 Novikov algebras
• On classification of four-dimensional nilpotent Leibniz algebras
• 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 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS
• Degenerations of binary Lie and nilpotent Malcev algebras
• 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
• Classification of 5-dimensional complex nilpotent Leibniz algebras
• The algebraic and geometric classification of nilpotent binary Lie algebras
• Degenerations of Leibniz and Anticommutative Algebras
• Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less than Five
• The Variety of Nilpotent Tortkara Algebras

This page was built for publication: The algebraic classification of nilpotent associative commutative algebras