8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields of char ≠ 2, 3

2025/07/20 by Giovanni Bazzoni, Bazzoni, Giovanni, Juan Rojo +1
Mathematics · #14M15 #15A75 #17B30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2507.14907

openalex publication_date 2025/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We provide a self contained, elementary, and geometrically-flavored classification of 8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields of characteristic ≠ 2,3, using the algebro-geometric arguments from \citeB and elementary linear algebra.

Citations

• Nilmanifolds with non-nilpotent complex structures and their pseudo-Kähler geometry
• Real non-degenerate two-step nilpotent Lie algebras of dimension eight
• Degenerations of 8-dimensional 2-step nilpotent Lie algebras
• Spin-harmonic structures and nilmanifolds
• Complex symplectic structures on Lie algebras
• A family of complex nilmanifolds with infinitely many real homotopy types
• Minimal algebras and 2-step nilpotent Lie algebras in dimension 7
• Classification of Minimal Algebras over any Field up to Dimension 6
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• On linear spaces of skew-symmetric matrices of constant rank

Related

• Minimal algebras and 2-step nilpotent Lie algebras in dimension 7
• Real non-degenerate two-step nilpotent Lie algebras of dimension eight
• Degenerations of 8-dimensional 2-step nilpotent Lie algebras
• Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
• A computer-based approach to the classification of nilpotent Lie\n algebras