Dynkin Diagrams and Root Systems of Indefinite Quasi-Hyperbolic Kac-Moody Algebra QHA4(2)

Objectives: To obtain the complete classification of a particular class of indefinite type of quasi hyperbolic Kac-Moody algebra QHA₄⁽²⁾ and to study the properties of imaginary ischolar_mains. Methods: Pure theoretical approach for the classification of Dynkin diagrams and an analytical approach for the ischolar_main 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 QHA₄⁽²⁾ is obtained. Here, the number of connected, non isomorphic Dynkin diagrams associated with QHA₄⁽²⁾ is 858. The properties of strictly imaginary and purely imaginary ischolar_mains are also studied for QHA₄⁽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.