Invariants of Lie algebras via moving frames

TL;DR

This paper presents an algebraic algorithm using moving frames to compute invariants of Lie algebras, including generalized Casimir operators, with applications to low-dimensional and solvable Lie algebras.

Contribution

It introduces a purely algebraic method for calculating Lie algebra invariants using moving frames, applicable to various algebra classes.

Findings

Algorithm effectively computes invariants of low-dimensional Lie algebras.

Method applies to series of solvable Lie algebras with specific nilradical structures.

Reviewed applications demonstrate the method's versatility.

Abstract

A purely algebraic algorithm for computation of invariants (generalized Casimir operators) of Lie algebras by means of moving frames is discussed. Results on the application of the method to computation of invariants of low-dimensional Lie algebras and series of solvable Lie algebras restricted only by a required structure of the nilradical are reviewed.