Math IntroSeries

June 30, July 1, 3, 8, & 10, 2025 

via Zoom

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18:00 - 19:30 • Philippine time

15:30 - 17:00 • India time

12:00 - 13:30 • Sweden time

11:00 - 12:30 • Portugal time

Abstract: 

This will be an introduction to the representation theory of infinite-dimensional algebras. The motivation will come from Lie theory as generalized Weyl algebras (GWA) encode the representation theory of several Lie algebras of small dimension. We will begin by discussing the Lie algebra sl₂ and its representations. This will motivate the definition of GWA, which will be accompanied by many examples of such, including (classical) Weyl algebras. Finally, we will approach the representation theory of GWAs through the notion of weight modules, which are inspired by Verma modules and more generally by category O for semisimple Lie algebras.