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### Dynkin Diagrams and Root Systems of Indefinite Quasi-Hyperbolic Kac-Moody Algebra QHA_{4}^{(2)}

#### Abstract

**Objectives:**To obtain the complete classification of a particular class of indefinite type of quasi hyperbolic Kac-Moody algebra QHA

_{4}

^{(2)}and to study the properties of imaginary roots.

**Methods:**Pure theoretical approach for the classification of Dynkin diagrams and an analytical approach for the root system are applied.

**Findings:**The complete classification of Dynkin diagrams associated to the Generalized Cartan Matrix of quasi hyperbolic indefinite type of Kac-Moody algebra QHA

_{4}

^{(2)}is obtained. Here, the number of connected, non isomorphic Dynkin diagrams associated with QHA

_{4}

^{(2)}is 858. The properties of strictly imaginary and purely imaginary roots are also studied for QHA

_{4}

^{(2)}.

**Applications:**Kac-Moody algebra has applications in various fields of mathematics and mathematical physics such as combinatorics, number theory, partial differential equations, quantum physics etc.

#### Keywords

Dynkin Diagram, Indefinite Quasi Hyperbolic, Kac-Moody Algebras, Purely Imaginary Roots, Strictly Imaginary Roots.

#### References

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