Lie subalgebras of so(3,1) up to conjugacy

Abstract

Purpose – This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1). Design/methodology/approach – The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions. Findings – The authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1). Originality/value – This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.

Keywords

• Simple Lie algebra
• Lie subalgebra
• Conjugate subalgebras