A Study on Dynkin Diagrams and Root System of Indefinite Quasi Affine Kac Moody Algebras QAD3(2)
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- Dynkin Diagrams, Generalized Cartan Matrix, Imaginary Roots, Kac Moody Algebras, Quasi Affine
- A. Uma Maheswari
- QAD3(2) represents the indefinite, quasi affine type of Kac Moody algebras, extended from the affine class D3(2). In this paper, the non isomorphic connected Dynkin diagrams associated with the family QAD3(2) are completely classified; among this classification of Dynkin diagrams of QAD3(2) the extended hyperbolic, quasi hyperbolic and indefinite but non extended, non quasi hyperbolic diagrams are identified; It is shown that the family QAD3(2) satisfies the purely imaginary property. Some of the basic properties of the root system i.e. the short and long real roots are identified; the minimal imaginary and imaginary roots are studied for three specific classes of quasi affine Kac Moody algebras belonging to the family QAD3(2); the short and long real roots are identified; some of the imaginary roots, minimal imaginary roots and isotropic roots have been explicitly given for this class of Kac Moody algebras; In all, there are 909 non isomorphic connected Dynkin diagrams associated with QAD3(2), within which Dynkin diagrams are of extended hyperbolic type, hyperbolic type, quasi hyperbolic diagrams and diagrams of indefinite, non extended hyperbolic type are identified.
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