# Algebra of Symmetry Operators for Klein-Gordon-Fock Equation

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Conditions for the Existence of Symmetry Operators

#### 2.1. Hamilton-Jacobi Equation

#### 2.2. Klein-Gordon-Fock Equation

**Statement**.

**Statement**is proved.

## 3. Solvable Groups ${\mathit{G}}_{\mathbf{3}}(\mathit{N})$

#### 3.1. The Group ${G}_{3}(I)$

#### 3.2. Group ${G}_{3}(II)$

#### 3.3. Group ${G}_{3}(III)$

#### 3.4. Group ${G}_{3}(IV)$

#### 3.5. Group ${G}_{3}(V).$

#### 3.6. Group ${G}_{3}(VI)$

#### 3.7. Group ${G}_{3}(VII)$

## 4. Insolvable Groups ${\mathbf{G}}_{\mathbf{3}}(\mathbf{N})$

#### 4.1. Group ${G}_{3}(VIII)$

#### 4.2. Group ${G}_{3}(IX)$

## 5. Conclusions

## Funding

## Conflicts of Interest

## Appendix A.

#### Appendix A.1. Group G_{3} (I)

#### Appendix A.2. Group G_{3} (II)

#### Appendix A.3. Group G_{3} (III)

#### Appendix A.4. Group G_{3} (IV)

#### Appendix A.5. Group G_{3} (V)

#### Appendix A.6. Group G_{3} (VI)

#### Appendix A.7. Group G_{3} (VII)

#### Appendix A.8. Group G_{3} (VIII)

#### Appendix A.9. Group G_{3} (IX)

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Obukhov, V.V.
Algebra of Symmetry Operators for Klein-Gordon-Fock Equation. *Symmetry* **2021**, *13*, 727.
https://doi.org/10.3390/sym13040727

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Obukhov VV.
Algebra of Symmetry Operators for Klein-Gordon-Fock Equation. *Symmetry*. 2021; 13(4):727.
https://doi.org/10.3390/sym13040727

**Chicago/Turabian Style**

Obukhov, Valeriy V.
2021. "Algebra of Symmetry Operators for Klein-Gordon-Fock Equation" *Symmetry* 13, no. 4: 727.
https://doi.org/10.3390/sym13040727