# Geometric and Differential Features of Scators as Induced by Fundamental Embedding

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Remark**

**1.**

- Product of time-like scator with time-like scator is still time-like.
- Product of two space-like scators is time-like.
- Product of space-like scator with time-like scator is space-like.
- Product of light-like scator with any scator is light-like.

**Definition**

**2.**

**Remark**

**2.**

**Remark**

**3.**

## 3. Geometry of Duality Automorphisms

**Definition**

**3.**

**Definition**

**4.**

**Theorem**

**1.**

**Proof.**

**Lemma**

**1.**

**Proof.**

## 4. Derivative with Respect to Scalar

**Definition**

**5.**

**Remark**

**4.**

**Lemma**

**2.**

**Proof.**

**Remark**

**5.**

**Corollary**

**1.**

## 5. Modified Leibniz Rule for Scators

**Theorem**

**2.**

**Proof.**

## 6. Hypercomplex Holomorphic Functions

## 7. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Kobus, A.; Cieśliński, J.L.
Geometric and Differential Features of Scators as Induced by Fundamental Embedding. *Symmetry* **2020**, *12*, 1880.
https://doi.org/10.3390/sym12111880

**AMA Style**

Kobus A, Cieśliński JL.
Geometric and Differential Features of Scators as Induced by Fundamental Embedding. *Symmetry*. 2020; 12(11):1880.
https://doi.org/10.3390/sym12111880

**Chicago/Turabian Style**

Kobus, Artur, and Jan L. Cieśliński.
2020. "Geometric and Differential Features of Scators as Induced by Fundamental Embedding" *Symmetry* 12, no. 11: 1880.
https://doi.org/10.3390/sym12111880