On the Geometry of the Hyperbolic Scator Space in

Authors: Artur Kobus Jan L Cieśliński

Publish Date: 2016/04/01

Volume: 27, Issue: 2, Pages: 1369-1386

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Abstract

We consider the scator space in 1+2 dimensions—a hypercomplex nondistributive hyperbolic algebra introduced by FernándezGuasti and Zaldívar We find a method for treating scators algebraically by embedding them into a distributive and commutative algebra A notion of dual scators is introduced and discussed We also study isometries of the scator space It turns out that 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 arise some open questions eg whether hypothetical tachyons can be considered as usual particles possessing timelike trajectoriesOpen AccessThis article is distributed under the terms of the Creative Commons Attribution 40 International License http//creativecommonsorg/licenses/by/40/ which permits unrestricted use distribution and reproduction in any medium provided you give appropriate credit to the original authors and the source provide a link to the Creative Commons license and indicate if changes were made

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