On solvable Lie algebras of small breadth

2025/07/01 by Borworn Khuhirun, Khuhirun, Borworn, Korkeat Korkeathikhun +5
Mathematics · #17B30 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2507.00602

openalex publication_date 2025/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie algebras of breadth less than or equal to 2. More importantly, we provide a complete classification of such Lie algebras that are pure and nonnilpotent over the complex numbers.

Citations

• On the problem of classifying solvable Lie algebras having small codimensional derived algebras
• Breadth and characteristic sequence of nilpotent Lie algebras
• On nilpotent Lie algebras of small breadth
• Solvable Lie A-algebras
• Classification of solvable Lie algebras

Related

• On nilpotent Lie algebras of small breadth
• A class of Solvable Lie algebras
• Classification of solvable Lie algebras
• Lie algebras with nilpotent length greater than that of each of their\n subalgebras
• Breadth and characteristic sequence of nilpotent Lie algebras