The geometric classification of 2-step nilpotent algebras and applications

DOI10.1007/s13163-021-00411-0OpenAlexW3210909097MaRDI QIDQ2674034

Yanyan Li

Publication date: 22 September 2022

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.01036

zbMATH Keywords

degenerationassociative algebrairreducible componentnilpotent algebrageometric classification2-step nilpotent algebra

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Deformations of associative rings (16S80) General nonassociative rings (17A99) Nonassociative algebras satisfying other identities (17A30) (non-Lie) Hom algebras and topics (17D30)

Related Items (6)

Derivations of two-step nilpotent algebras ⋮ The algebraic and geometric classification of transposed Poisson algebras ⋮ Degenerations of noncommutative Heisenberg algebras ⋮ The geometric classification of nilpotent algebras ⋮ Non-degenerate evolution algebras ⋮ The algebraic and geometric classification of antiassociative algebras

Cites Work

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• Varieties of nilpotent Lie algebras of dimension less than six
• The algebraic and geometric classification of associative algebras of dimension five
• Classification of orbit closures of 4-dimensional complex Lie algebras
• Lie bialgebra structures on 2-step nilpotent graph algebras
• Pseudo-metric 2-step nilpotent Lie algebras
• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• The algebraic and geometric classification of nilpotent assosymmetric algebras
• Degenerations of 8-dimensional 2-step nilpotent Lie algebras
• Some classes of nilpotent associative algebras
• Canonical matrices of bilinear and sesquilinear forms
• Algebraic geography: Varieties of structure constants
• On the deformation of rings and algebras
• 2-Nilpotent and Rigid Finite Dimensional Algebras
• On the classification of bilinear maps with radical of a fixed codimension
• Corrigendum to ‘Degenerations of Zinbiel and nilpotent Leibniz algebras’
• Complete classification of algebras of level two
• On geometric degenerations and Gerstenhaber formal deformations
• Degenerations of nilpotent associative commutative algebras
• The classification of 5-dimensional complex nilpotent associative algebras
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