Topic Proposal : Semisimple Lie Algebras and Their Representations

نویسندگان

  • Apoorva Khare
  • Victor Ginzburg
چکیده

In this topic proposal, we discuss the representation theory of semisimple Lie algebras, including results on the structure of these algebras and their modules. In particular, the theory of root systems and Verma modules are very important in this context. We classify all simple Lie algebras, and obtain a presentation for any semisimple Lie algebra. We also encounter several striking formulas that help us learn more about the structure of the modules. We describe certain lattices in the modules, and related groups. Mostly we work over algebraically closed fields of characteristic zero, but some constructions extend to arbitrary fields as well.

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تاریخ انتشار 2002