A Note on the Representation and Definition of Dual Split Semi-quaternions Algebra

Abstract

In this paper, dual split semi-quaternions algebra, ss Η , is defined for the first time, and some fundamental algebraic properties of its is studied. The set of all unit dual split semi-quaternions is a subgroup of ss Η . Fortheremore, by De-Moivre’s formula, any powers of these quaternions are obtained.