Vector generators of the real Clifford algebras

Abstract

In this paper, we introduce a method to obtain vector generators for the real matrix representation L p, q of the real Clifford algebra C l p, q from the real matrix representation L2n ( R) of C l 0, n with n = p+ q for every n. N. This can give a nice tool to classify the Clifford algebra C l p, q in the sense of generators. Also, we present the inverse of a nonzero vector in L2n ( R) and using the properties of vector generators in L p, q, we obtain some results about determinant and inverse of a vector in Ln- 1,1. Moreover, we show the relations of solutions for the linear equation xa = ax for some a. Delta in L0,2 and that for xb = bx in L p, q for some b. L p, q, where p + q = 2.