#
On l_{p}-Complex Numbers

## Abstract

**:**

## 1. Introduction

## 2. Definition and Basic Properties of ${l}_{p}$-Complex Numbers

**Definition**

**1.**

**Definition**

**2.**

**Remark**

**1.**

**Proof.**

**Remark**

**2.**

## 3. Invariant Transformations

**Theorem**

**1.**

**Proof.**

**Remark**

**3.**

## 4. Generalizing Euler’s Trigonometric Representation

**Definition**

**3.**

**Remark**

**4.**

**Definition**

**4.**

**Theorem**

**2.**

**Proof.**

**Definition**

**5.**

**Definition**

**6.**

**Theorem**

**3.**

**Proof.**

## 5. Discussion

## Funding

## Conflicts of Interest

## References

- Ebbinghaus, H.-D.; Hermes, H.; Hirzebruch, F.; Koecher, M.; Mainzer, K.; Neukirch, J.; Prestel, A.; Remmert, R. Numbers; Springer: Berlin, Germany, 1991. [Google Scholar]
- Hieber, M. Analysis I; Springer: Berlin, Germany, 2018. [Google Scholar]
- Krasnov, M.A.; Kiselev, A.; Shikin, G.M.E. Mathematical Analysis for Engineers; Mir Publishers: Moscow, Russia, 1990; Volume I. [Google Scholar]
- Mallik, A. The Story of Numbers; World Scientific Publishing: Singapore, 2018. [Google Scholar]
- Schmid, H. Elementare Technomathematik; Springer: Berlin, Germany, 2018. [Google Scholar]
- Atiyah, M.F.; Bott, R.; Shapiro, A. Clifford modules. Topology
**1964**, 3, 3–38. [Google Scholar] - Brauer, R.; Weyl, H. Spinors in n dimensions. Am. J. Math.
**1935**, 57, 425–449. [Google Scholar] [CrossRef] - Cartan, E. Lecons Sur le Théorie des Spineurs; Hermann: Paris, France, 1938. [Google Scholar]
- Chevalley, C. The Algebraic Theory of Spinors; Columbia Press: New York, NY, USA, 1954. [Google Scholar]
- Richter, W.-D. Generalized spherical and simplicial coordinates. J. Math. Anal. Appl.
**2007**, 336, 1187–1202. [Google Scholar] [CrossRef] [Green Version] - Moszyńska, M.; Richter, W.-D. Reverse triangle inequality. Antinorms and semi-antinorms. Stud. Sci. Math. Hung.
**2012**, 49, 120–138. [Google Scholar] [CrossRef] - Sasvári, Z. Multivariate Characteristic and Correlation Functions; De Gruyter: Berlin, Germany, 2013. [Google Scholar]

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Richter, W.-D.
On *l*_{p}-Complex Numbers. *Symmetry* **2020**, *12*, 877.
https://doi.org/10.3390/sym12060877

**AMA Style**

Richter W-D.
On *l*_{p}-Complex Numbers. *Symmetry*. 2020; 12(6):877.
https://doi.org/10.3390/sym12060877

**Chicago/Turabian Style**

Richter, Wolf-Dieter.
2020. "On *l*_{p}-Complex Numbers" *Symmetry* 12, no. 6: 877.
https://doi.org/10.3390/sym12060877