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Mathematics and Statistics Colloquium

Date/Time/Room: Friday (10/26/2007) at 2:30pm in 304 Pickard Hall

Speaker: Dr. Vyjayanthi Chari, Professor
Department of Mathematics, University of California at Riverside.
(Local host: M. Vancliff)

"Quivers and Current Algebras Associated to Simple Lie Algebras"

Abstract: A quiver is a directed graph; in other words, it is a pair (Q₀; Q₁) where Q₀ is a collection of vertices and Q₁ is a collection of arrows between the vertices. One can associate to a quiver Q, in a natural way, an algebra KQ over a field K; this algebra is called the path algebra of Q, and, under some very simple conditions, it is a finite-dimensional unital algebra. A current algebra is the Lie algebra consisting of polynomial maps from the complex numbers to a simple Lie algebra; in particular, the current algebra is an infinite-dimensional Lie algebra. We shall see that there is a remarkable connection between the representation theory of current algebras and representations of quivers satisfying certain relations.

Note that there will be an AGANT talk the same day at UTA at 4:30 pm by the same speaker. Please see http://www.uta.edu/math/pages/main/seminar.htm#agant for more details. Refreshments will be served in PKH 304 between the two talks.