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

Autor: Jan L. Cieśliński, Dzianis Zhalukevich
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Symmetry, Vol 12, Iss 9, p 1550 (2020)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym12091550
Popis: 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 (1+2)-dimensional scator space.
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