# On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Background

## 3. Preliminaries

**Definition**

**1.**

- (i)
- $D({\vee}^{p}({\Omega}_{n}(R)))\subset {\vee}^{p+1}({\Omega}_{n}(R))$
- (ii)
- D is an n-th order derivation over k and
- (iii)
- the restriction of D to R ($R\simeq {\vee}^{0}({\Omega}_{n}(R))$) is the Kähler derivation $\phantom{\rule{4pt}{0ex}}{d}_{n}:R\to {\Omega}_{n}(R).$

**Lemma**

**1.**

**Proof**

**of**

**Lemma**

**1**.

**Proposition**

**1.**

## 4. Main Results

**Lemma**

**2.**

**Proof**

**of**

**Lemma**

**2.**

**Lemma**

**3.**

**Proof**

**of**

**Lemma**

**3.**

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Example**

**1.**

**Example**

**2.**

## 5. Discussion

- (1)
- Can I define a new approach related to high order symmetric and exterior derivations of Kähler modules?
- (2)
- Under which conditions can I write a connection about high order symmetric and exterior derivations on Kähler modules.

## 6. Conclusions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Merkepçi, H.
On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules. *Symmetry* **2018**, *10*, 365.
https://doi.org/10.3390/sym10090365

**AMA Style**

Merkepçi H.
On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules. *Symmetry*. 2018; 10(9):365.
https://doi.org/10.3390/sym10090365

**Chicago/Turabian Style**

Merkepçi, Hamiyet.
2018. "On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules" *Symmetry* 10, no. 9: 365.
https://doi.org/10.3390/sym10090365