On the geometry of the hyperbolic scator space in \(1+2\) dimensions (Q2361392)

For the non-distributive hypercomplex \(3\)-dimensional algebra introduced in [\textit{M. Fernández-Guasti} and the reviewer, Adv. Appl. Clifford Algebras 23, No. 3, 639--656 (2013; Zbl 1330.17008)], the authors study isometric properties of this algebra by introducing a sort of dualization which preserves the scator product and is an isometry for the \(3\)-dimensional hyperbolic scator space. More interesting, the authors find a multiplicative embedding of the hyperbolic \(3\)-dimensional scator space in a \(4\)-dimensional commutative, associative and distributive real algebra. The paper ends with a few remarks on applications of these constructions for some variations of special relativity and the possible existence of more interesting dualities.