An Algorithm for Determining Lie Algebra Types

TL;DR

This paper introduces an explicit algorithm, implemented in Matlab, for determining the type of finite dimensional complex Lie algebras based on their Jordan--Kronecker invariants.

Contribution

It provides a novel, practical algorithm for classifying Lie algebra types from invariants, enhancing computational methods in Lie algebra theory.

Findings

Algorithm successfully classifies Lie algebra types

Implementation in Matlab demonstrates practical usability

Advances computational tools for Lie algebra analysis

Abstract

This paper investigates the Jordan--Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra from its Jordan--Kronecker invariant. The algorithm is implemented in a specific Matlab program.