UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (10/8/2004) at 4:00pm in 487 Pickard Hall

Speaker: Matt Summers, Bell Helicopter Textron Inc.

"Line Modules Over a Family of Four-Dimensional Regular Algebras"

Abstract: The connected, regular algebras of global dimension three were classified in the late 1990s, primarily through the work of M. Artin, W. Schelter, J. Tate, and M. Van Den Bergh. This was made possible by associating certain graded modules to geometric objects, such as "point modules" to points, "line modules" to lines, etc. It is widely believed that this technique will play a major role in classifying the regular algebras of global dimension four. In this talk we will present a family of such algebras and classify all line modules over these algebras. Included in this family is the quantum universal enveloping algebra of the Lie algebra sl(2), which has many applications in mathematics and physics.