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Mathematics and Statistics Colloquium
Date/Time/Room:
Friday (10/26/2007) at 2:30pm in 304 Pickard Hall "Quivers and Current Algebras Associated to Simple Lie Algebras"Abstract: A quiver is a directed graph; in other words, it is a pair (Q_{0}; Q_{1}) where Q_{0} is a collection of vertices and Q_{1} 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 finitedimensional 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 infinitedimensional 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.

