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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/9/1550 |
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| author | Jan L. Cieśliński Dzianis Zhalukevich |
| author_facet | Jan L. Cieśliński Dzianis Zhalukevich |
| author_sort | Jan L. Cieśliński |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:11:52Z |
| format | Article |
| id | doaj.art-b4594672c44f4016b86904a0082ae6b2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T16:11:52Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b4594672c44f4016b86904a0082ae6b22023-11-20T14:23:13ZengMDPI AGSymmetry2073-89942020-09-01129155010.3390/sym12091550Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional CaseJan L. Cieśliński0Dzianis Zhalukevich1Wydział Fizyki, Uniwersytet w Białymstoku, ul. Ciołkowskiego 1L, 15-245 Białystok, PolandWydział Fizyki, Uniwersytet w Białymstoku, ul. Ciołkowskiego 1L, 15-245 Białystok, PolandScators 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.https://www.mdpi.com/2073-8994/12/9/1550scatorsholomorphic functionsgeneralized Cauchy–Riemann equations |
| spellingShingle | Jan L. Cieśliński Dzianis Zhalukevich Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case Symmetry scators holomorphic functions generalized Cauchy–Riemann equations |
| title | Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case |
| title_full | Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case |
| title_fullStr | Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case |
| title_full_unstemmed | Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case |
| title_short | Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case |
| title_sort | explicit formulas for all scator holomorphic functions in the 1 2 dimensional case |
| topic | scators holomorphic functions generalized Cauchy–Riemann equations |
| url | https://www.mdpi.com/2073-8994/12/9/1550 |
| work_keys_str_mv | AT janlcieslinski explicitformulasforallscatorholomorphicfunctionsinthe12dimensionalcase AT dzianiszhalukevich explicitformulasforallscatorholomorphicfunctionsinthe12dimensionalcase |