Singh , Amit Kumar (2011) *Some studies on dynkin diagrams associated with Kac-moody algebra.* MSc thesis.

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## Abstract

In the present project report, a sincere report has been made to construct and study the basic information related to Simple Lie Algebras, Kac-Moody algebras and their corresponding Dynkin Diagrams.

In chapter-1, I have given the definitions of Lie Algebra and some of the terms related to Lie algebra, i.e. subalgebras, ideals, Abelian, solvability, nilpotency etc. Also, I have done the classifications of Classical Lie algebras.

In chapter-2, I addressed the basics of Representation Theory, i.e. structure constants, modules, reflections in a Euclidean space, root systems (simple roots) and their corresponding root diagrams. Then I have discussed the formation of Dynkin Diagrams and cartan matrices associated with the roots of the simple lie algebras.

In chapter-3, I have given the necessary theory based on Kac-Moody lie algebras and their classifications. Then the definition of the extended Dynkin diagrams for Affinization of Kac-Moody algebras and the Dynkin Diagrams associated with the affine Kac-Moody algebras are provided

Item Type: | Thesis ( MSc) |
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Uncontrolled Keywords: | Kac-moody algebra, roots, dynkin diagrams |

Subjects: | Mathematics and Statistics > Topology |

Divisions: | Sciences > Department of Mathematics |

ID Code: | 2195 |

Deposited By: | SINGH AMIT KUMAR KK |

Deposited On: | 13 May 2011 09:20 |

Last Modified: | 13 May 2011 09:47 |

Supervisor(s): | Pati, K C |

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