A. Uma Maheswari ¹, S. Krishnaveni ²

Affiliations
1 Department of Mathematics, Quaid-E-Millath Government College for Women (Autonomous), Chennai - 600002, Tamil Nadu, IN
2 Department of Mathematics, M.O.P Vaishnav College for Women (Autonomous), Chennai - 600034, Tamil Nadu, IN

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 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.

Keywords

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

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