#
On the Solvability of ℤ_{3}-Graded Novikov Algebras

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Preliminary Calculations

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Corollary**

**1.**

**Proof.**

## 3. ${\mathbb{Z}}_{2}$-Graded Novikov Algebra with Solvable Even Part

**Corollary**

**2.**

**Proof.**

**Proposition**

**1.**

**Lemma**

**3.**

**Proof.**

**Lemma**

**4.**

**Proof.**

**Lemma**

**5.**

**Proof.**

**The**

**Proof**

**of**

**Proposition**

**1.**

**Theorem**

**1.**

**Proof.**

**Example**

**1.**

## 4. Some Ideals of ${\mathbb{Z}}_{3}$-Graded Novikov Algebras

**Lemma**

**6.**

**Proof.**

**Lemma**

**7.**

**Proof.**

## 5. ${\mathbb{Z}}_{3}$-Graded Novikov Algebras with Solvable 0-Component

**Proposition**

**2.**

**Corollary**

**3.**

**Lemma**

**8.**

**Proof.**

**Lemma**

**9.**

**Proof.**

**Lemma**

**10.**

**Proof.**

**Lemma**

**11.**

**Proof.**

**The**

**Proof**

**of**

**the**

**Proposition**

**2.**

**Theorem**

**2.**

**Proof.**

**Corollary**

**4.**

**Corollary**

**5.**

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Zhelyabin, V.; Umirbaev, U.
On the Solvability of ℤ_{3}-Graded Novikov Algebras. *Symmetry* **2021**, *13*, 312.
https://doi.org/10.3390/sym13020312

**AMA Style**

Zhelyabin V, Umirbaev U.
On the Solvability of ℤ_{3}-Graded Novikov Algebras. *Symmetry*. 2021; 13(2):312.
https://doi.org/10.3390/sym13020312

**Chicago/Turabian Style**

Zhelyabin, Viktor, and Ualbai Umirbaev.
2021. "On the Solvability of ℤ_{3}-Graded Novikov Algebras" *Symmetry* 13, no. 2: 312.
https://doi.org/10.3390/sym13020312