Solvable Lie algebras with triangular nilradicals

TL;DR

This paper constructs all finite-dimensional indecomposable solvable Lie algebras with a triangular nilradical, detailing their structure and the relationship between their nonnilpotent elements and dimension.

Contribution

It provides a complete classification of such Lie algebras, explicitly constructing them and analyzing their parameters and dimensions.

Findings

Number of nonnilpotent elements ranges from 1 to n-1

Dimension formula for the Lie algebras is established

Explicit construction of all indecomposable cases

Abstract

All finite-dimensional indecomposable solvable Lie algebras $L(n,f)$, having the triangular algebra T(n) as their nilradical, are constructed. The number of nonnilpotent elements $f$ in $L(n,f)$ satisfies $1\leq f\leq n-1$ and the dimension of the Lie algebra is $\dim L(n,f)=f+{1/2}n(n-1)$.