Root System and Dynkin Diagrams for the General Class of Indefinite Quasi Affine Kac Moody Algebras QAG2(1)

Research Area: Volume 5,Issue 1, Jan. 2016 Year: 2016
Type of Publication: Article Keywords: Dynkin Diagrams, Imaginary Roots, Kac Moody Algebras, Quasi Affine
Authors:
  • A. Uma Maheswari
Journal: IJEIR Volume: 5
Number: 1 Pages: 59-65
Month: January
ISSN: 2277-5668
Abstract:
In this paper the general class of indefinite quasi affine Kac Moody algebras QAG2(1) are considered. The root system of this family is studied; in particular, the short and long real roots are obtained and some of the basic properties of imaginary roots are studied for a particular class. This class is found to satisfy the purely imaginary property, i.e. all the imaginary roots are purely imaginary; isotropic and minimal imaginary roots are computed for a particular class of quasi affine Kac Moody algebras belonging to the family QAG2(1). The complete set of connected, non isomorphic Dynkin diagrams of QAG2(1), where an extended vertex is connected to either one, two or all three vertices of the base affine family G2(1) is given. This classification is the generalization of the one obtained earlier, wherein, only the case where the extended vertex of QAG2(1) is connected to all the three vertices of the affine family G2(1). Among this set of diagrams, the extended hyperbolic type and diagrams of indefinite, non extended hyperbolic type are identified.

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