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
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 KacMoody 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).