Generalized quaternions and their algebraic properties

Abstract

C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 6 4 , N u m b e r 1 , P a g e s 1 5-2 7 (2 0 1 5) D O I: 1 0 .1 5 0 1 / C o m m u a 1 _ 0 0 0 0 0 0 0 7 2 4 IS S N 1 3 0 3-5 9 9 1 Abstract. The aim of this paper is to study the generalized quaternions, H ; and their basic properties. H has a generalized inner product that allows us to identify it with four-dimensional space E 4 : Also, it is shown that the set of all unit generalized quaternions with the group operation of quaternion multiplication is a Lie group of 3-dimension and its Lie algebra is found.