A Vogan diagram is a Dynkin diagram of triplet (gR; h0;4+), where gR is a real Lie algebras, h0 Cartan subalgebra, 4+ positive root system. Vogan diagrams are useful tools to classify the real forms of a Lie algebras, affine Kac-Moodyudalgebras (both twisted and untwised). In our thesis we have classified Vogan diagrams for some hyperbolic Kac-Moody algebras which have potential physical application. The real forms of Lie Superalgebra, affine twisted and untwisted Kac-Moody superalgebras are also classified by Vogan diagrams. In our last Chapter we have also included the construction of splints of Lie superalgebras and discussed defining relations and flip super dynkin diagrams related with root system.
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