Extension of algebras and its applications to the real Clifford algebras

Abstract

Extension of algebras can be constructed through various manners. In this paper, we introduce a new way of construction to extend a given algebra of dimension 2(n), which is isomorphic to the real Clifford algebra Cl-0,Cl-n, to another algebra of dimension 2(n+1) over the real numbers. And then, we generalize the construction over a Z(2)-grading algebra. Moreover, we will show the relation between the new constructed algebras and Clifford algebras.