Matrix representations of the real clifford algebras of order four

Abstract

As a consequence of the previous paper [7], we know that the matrix subalgebra L0, 4 with real entries is isomorphic to the real Clifford algebra Cℓ0, 4. In this paper, we introduce a method to induce the real matrix representations of all the real Clifford algebras of order 4 by multiplying some specific diagonal matrices to the vector generators of L0, 4. Also, we define the matrix subalgebra with complex entries which is isomorphic to the real Clifford algebra Cℓ0, 4. Finally, we induce the complex matrix representations of all the real Clifford algebras of order 4 similarly as in the real case. © 2013 Pushpa Publishing House, Allahabad, India.