Geometric and Differential Features of Scators as Induced by Fundamental Embedding

Autor: Artur Kobus, Jan L. Cieśliński
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Symmetry, Vol 12, Iss 11, p 1880 (2020)
Druh dokumentu: article
ISSN: 12111880
2073-8994
DOI: 10.3390/sym12111880
Popis: The scator space, introduced by Fernández-Guasti and Zaldívar, is endowed with a product related to the Lorentz rule of addition of velocities. The scator structure abounds with definitions calculationally inconvenient for algebraic operations, like lack of the distributivity. It occurs that situation may be partially rectified introducing an embedding of the scator space into a higher-dimensonal space, that behaves in a much more tractable way. We use this opportunity to comment on the geometry of automorphisms of this higher dimensional space in generic setting. In parallel, we develop commutative-hypercomplex analogue of differential calculus in a certain, specific low-dimensional case, as also leaned upon the notion of fundamental embedding, therefore treating the map as the main building block in completing the theory of scators.
Databáze: Directory of Open Access Journals
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