On certain decompositions of solvable Lie algebras

TL;DR

This paper explores a broader class of solvable Lie algebras that generalizes previous decompositions, demonstrating that these algebras can be expressed as a direct sum of abelian subalgebras with well-structured ideals.

Contribution

It introduces a new class of solvable Lie algebras encompassing previous classes, extending known decomposition results to this larger class.

Findings

Decomposition as a vector space direct sum of abelian subalgebras

Ideals relate to the decomposition in a structured way

The new class contains both solvable Lie A-algebras and complemented solvable Lie algebras

Abstract

The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of these classes is contained in the other. The object of this paper is to find a larger class of algebras, containing each of these classes, in which these same results hold.