**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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