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

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.