UM Math Graduate Students Seminar

Christopher Harris
University of Miami

will present

Some Infinite Dimensional Groups and Algebras

Friday, September 30, 2011, 4:00pm
Ungar Building Room 402

Abstract:After briefly reviewing the notions of Lie groups and Lie algebras we will introduce the idea of a loop group. These are also Lie groups since they have a group structure and the structure of infinite-dimensional manifolds. We will then discuss their Lie algebras, loop algebras, and construct their central extensions which are known as (untwisted) affine Lie algebras. If we have time, we will also discuss the diffeomorphism group of the circle and the Virasoro algebra. All of these notions are essential in many parts of physics, especially string theory.

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