Matrix Representations of the Low Order Real Clifford Algebras

Abstract

In this paper we construct the matrix subalgebras of the real matrix algebra when 2 a parts per thousand currency sign r + s a parts per thousand currency sign 3 and we show that each is isomorphic to the real Clifford algebra . In particular, we prove that the algebras can be induced from when 2 a parts per thousand currency sign r + s = n a parts per thousand currency sign 3 by deforming vector generators of to multiply the specific diagonal matrices. Also, we construct two subalgebras and of matrix algebras and , respectively, which are both isomorphic to the Clifford algebra , and apply them to obtain the properties related to the Clifford group I"(0,3).