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Kac -Moody Algebras and Quantum Groups

Department of Mathematics & Statistics. Kac -Moody Algebras and Quantum Groups. Presenter: Dr. Adriano Adrega de Moura Place: BR Hall, Room 161 Time: 3:00pm – 4:00pm Date: Friday, January 28 Tea Time: 2:30pm.

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Kac -Moody Algebras and Quantum Groups

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  1. Department of Mathematics & Statistics Kac-Moody Algebras and Quantum Groups Presenter: Dr. Adriano Adrega de MouraPlace: BR Hall, Room 161Time: 3:00pm – 4:00pmDate: Friday, January 28 Tea Time: 2:30pm Lie algebras and quantum groups are mathematical objects with a wide range of applications in several areas of mathematics and physics. This is an introductory talk aimed especially at graduate students. We will review the concepts of Lie algebras and Serre's theorem on the classification of finite-dimensional semisimple Lie algebras over the field of complex numbers. This will naturally lead us to the definition of Kac-Moody algebras. We will then present the definition of the quantized universal enveloping algebra (quantum group) of a given Kac-Moody algebra. We shall end the talk with a brief survey of recent results obtained by the speaker and D. Jakelic on the finite-dimensional representations of quantum affine algebras (the quantum groups associated to Kac-Moody algebras of affine type).

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