Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements

TL;DR

This paper thoroughly investigates the invariants of a class of solvable Lie algebras with specific nilradicals and diagonal elements, introducing an algebraic algorithm for their construction.

Contribution

It presents a novel algebraic algorithm based on Cartan's method to explicitly construct invariants of these Lie algebras.

Findings

Explicit bases of invariants for all such algebras are obtained.

The algebraic algorithm simplifies the process of finding invariants.

The method is applicable to a broad class of solvable Lie algebras.

Abstract

The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on Cartan's method of moving frames.