Abstract
In this paper, we show that PO(2, 1) can be represented by invertible split quaternions. We introduce the concepts of t-similarity and t-pseudosimilarity of split quaternions. By such two similarities, we obtain several equivalence relations in split quaternions. We also show that a and b are semisimilar if and only if a2 and b2 are similar.
2010 Mathematics Subject Classifications:
Acknowledgments
The authors would like to express their deep gratitude to the referee and the handling editor for carefully reading this paper and some useful suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).