The algebraic classification of nilpotent algebras

Abstract

We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.

arXiv admin note: text overlap with arXiv:2006.00734, arXiv:2001.00253

References in corpus (17)

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• The variety of $2$-dimensional algebras over an algebraically closed field
• Classification of five-dimensional nilpotent Jordan algebras
• Degenerations of Zinbiel and nilpotent Leibniz algebras
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• Degenerations of nilpotent algebras
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• The geometric classification of Leibniz algebras
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Cited by in corpus (10)

• Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures
• Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equations
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent terminal algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent Novikov algebras
• The algebraic classification of nilpotent commutative algebras
• Lie algebroids. Lie-Rinehart algebras