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

Affiliations

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

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.

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