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On the Product Rule for the Hyperbolic Scator Algebra
Version 1
: Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (10:08:38 CEST)
A peer-reviewed article of this Preprint also exists.
Cieśliński, J.L.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Axioms 2020, 9, 55, doi:10.3390/axioms9020055. Cieśliński, J.L.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Axioms 2020, 9, 55, doi:10.3390/axioms9020055.
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.
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