Tensor product decompositions of the real clifford algebra

Abstract

In this paper, we present some methods to decompose the Clifford algebra Cl<inf>p,q</inf> into some Clifford algebras via tensor product by using the vector generators of Cl<inf>0, p</inf>, Cl<inf>0,q</inf> and Cl<inf>p,0</inf> In particular, we prove that Cl<inf>n−k+1,k−1</inf> is isomorphic to Cl<inf>0,n k+1</inf> ⊗ Cl<inf>0,k−1</inf> if k −1= 2t for some odd number t and Cl<inf>n−k+1,k−1</inf> is isomorphic to Cl<inf>n-k+1, 0</inf> ⊗ CA0, k−1 if k − 1 = 2t for some even number t. Furthermore, we apply those results to matrix representations of the real Clifford algebras.a. © 2015 Pushpa Publishing House, Allahabad, India.