On the Semisimilarity and Consemisimilarity of Split Quaternions

In this study, we introduce the concept of semisimilarity and consemisimilarity of split quaternions. Moreover, we examine the solvability conditions and general solutions of systems xay=b,ybx=aandx~ay=b,y~bx=a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${xay=b,ybx=a {\rm and} \widetilde{x}ay=b,\widetilde{y}bx=a}$$\end{document} in split quaternions. If there exist x and y that satisfy first equations system, then a and b are said to be semisimilar, if there exist x and y that satisfy second equations system, then a and b are said to be consemisimilar.