Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

How to cite: Cieśliński, J.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Preprints 2020, 2020040496 (doi: 10.20944/preprints202004.0496.v1). Cieśliński, J.; Kobus, A. On the Product Rule for the Hyperbolic Scator Algebra. Preprints 2020, 2020040496 (doi: 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.

Subject Areas

scators; non-distributive algebras; Lorentz velocity addition formula; fundamental embedding

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