Indian Journal of Science and Technology

Abstract

Objectives: To define the class of quasi affine generalized Kac-Moody algebras QAGGD3 (2), completely classify the non isomorphic, connected Dynkin diagrams associated with QAGGD3 (2) and compute some root multiplicities for this family. Methods: The representation theory of Kac-Moody algebras is applied to compute the multiplicities of roots for a quasi affine family in QAGGD3 (2). Findings: The quasi affine generalized Kac-Moody algebras associated with symmetrizable Generalized Generalized Cartan Matrices (GGCM) of quasi affine type, obtained from the affine family D3 (2), are defined; The connected, non-isomorphic Dynkin diagrams associated with this particular family are completely classified’; Multiplicities of roots of a class GKM algebras QAGGD3 (2), with one simple imaginary root are then determined using the representation theory of Kac Moody algebras; Application: Generalized Kac-Moody algebras find interesting applications in bosonic string theory, classifications in vertex operator theory , monstrous moonshine theory etc.
Keywords: Dynkin Diagram, Generalized Kac Moody Algebras (GKM), Imaginary Roots, Quasi Affine, Root Multiplicity