On geometry of the scator space

Abstract

We consider the scator space - a hypercomplex, non-distributive hyperbolic algebra introduced by Fern\'andez-Guasti and Zald\'ivar. We discuss isometries of the scator space and find consequent method for treating them algebraically, along with scators themselves. It occurs that introduction of zero divisors cannot be avoided while dealing with these isometries. The scator algebra may be endowed with a nice physical interpretation, although it suffers from lack of some physically demanded important features. Despite that, there arises some open questions, e.g., whether hypothetical tachyons can be considered as usual particles possessing time-like trajectories.