On Conjugacy of Maximal Subalgebras of Solvable Lie Algebras

TL;DR

This paper investigates the conditions under which two maximal subalgebras of a finite-dimensional solvable Lie algebra are conjugate and explores their intersections.

Contribution

It provides new criteria for conjugacy of maximal subalgebras and analyzes their intersections within solvable Lie algebras.

Findings

Criteria for conjugacy of maximal subalgebras established

Characterization of intersections of maximal subalgebras

Insights into the structure of solvable Lie algebras

Abstract

The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra $L$ are conjugate, and to investigate their intersection.