A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebras

TL;DR

This paper introduces new formulas for Clifford algebra elements and classifies 12 types of subalgebras within Lie algebras of pseudounitary groups using Clifford algebra techniques.

Contribution

It provides a novel classification of subalgebras of Lie algebras of pseudounitary groups based on Clifford algebra formulas.

Findings

12 types of subalgebras identified

New formulas for commutators and anticommutators

Clifford algebra techniques applied to Lie algebra classification

Abstract

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudounitary groups. Our main techniques are Clifford algebras. We have find 12 types of subalgebras of Lie algebras of pseudounitary groups.