On solvable Lie algebras of small breadth

TL;DR

This paper classifies finite-dimensional solvable Lie algebras over complex numbers with breadth ≤ 2, providing a complete characterization of pure, nonnilpotent cases, advancing understanding of their structure.

Contribution

It offers a complete classification of solvable Lie algebras of small breadth, specifically for pure, nonnilpotent cases over complex numbers, which was previously unexplored.

Findings

Classification of solvable Lie algebras with breadth ≤ 2

Characterization of pure, nonnilpotent Lie algebras over complex numbers

Structural insights into small-breadth solvable Lie algebras

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.