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Graduate Algebra and Representation Theory Seminar

Classification and Representation Theory of Semisimple Lie Algebras (1/2)

Songhao Zhu - Rutgers University

Location:  GSL - Hill 701
Date & time: Monday, 07 October 2019 at 3:10PM - 4:10PM

Abstract: We will review the root space decomposition of semisimple Lie algebras and the notion of root system discussed by the last speaker with one or two motivating examples, and use Dynkin diagram to introduce the classification result of all simple Lie algebras. Weyl group will be defined without too many technicalities. We will also give a uniform way (Serre's Theorem) to construct semisimple Lie algebras with the help of universal enveloping algebra, which serves as a tool to study the representation theory of semisimple Lie algebras.