Version 1
: Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (10:08:38 CEST)
How to cite:
Cieśliński, J.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Preprints2020, 2020040496. https://doi.org/10.20944/preprints202004.0496.v1
Cieśliński, J.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Preprints 2020, 2020040496. https://doi.org/10.20944/preprints202004.0496.v1
Cieśliński, J.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Preprints2020, 2020040496. https://doi.org/10.20944/preprints202004.0496.v1
APA Style
Cieśliński, J., & Kobus, A. (2020). On the Product Rule for the Hyperbolic Scator Algebra. Preprints. https://doi.org/10.20944/preprints202004.0496.v1
Chicago/Turabian Style
Cieśliński, J. and Artur Kobus. 2020 "On the Product Rule for the Hyperbolic Scator Algebra" Preprints. https://doi.org/10.20944/preprints202004.0496.v1
Abstract
Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension $1+2$ and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreove, we propose an extension of the scator product on the whole scator space, including scators with vanishing scalar component.
Keywords
scators; non-distributive algebras; Lorentz velocity addition formula; fundamental embedding
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.