Indian Journal of Science and Technology

Abstract

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