Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case

Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of holo...

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Bibliographic Details
Main Authors: Jan L. Cieśliński, Dzianis Zhalukevich
Format: Article
Language:English
Published: MDPI AG 2020-09-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/12/9/1550
Description
Summary:Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of holomorphicity. Until now, only a few particular cases of scator holomorphic functions have been found. In this paper we obtain all solutions of the generalized Cauchy–Riemann system which describes analogues of holomorphic functions in the <inline-formula><math display="inline"><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-dimensional scator space.
ISSN:2073-8994