Application of the method of quaternion typification for finding subalgebras and Lie subalgebras of Clifford algebras

TL;DR

This paper advances the quaternion typification method for Clifford algebra elements, enabling the identification of subalgebras and Lie subalgebras, and revealing new algebraic properties.

Contribution

It introduces a new classification of Clifford algebra elements that facilitates discovering subalgebras and Lie subalgebras, expanding understanding of Clifford algebra structure.

Findings

Identified new subalgebras of Clifford algebra

Found Lie subalgebras of the Clifford algebra

Discovered properties of subalgebras of the pseudo-unitary Lie group

Abstract

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous papers. On the basis of new classification of Clifford algebra elements it is possible to find out and prove a number of new properties of Clifford algebra. In particular, we find subalgebras and Lie subalgebras of Clifford algebra and subalgebras of the Lie algebra of the pseudo-unitary Lie group.