18 Dezembro 2020, 11:00 • Pedro Resende
Conclusion of the proof of the classification theorem. This lecture followed section 9.7 Brian Halls' book.
17 Dezembro 2020, 11:00 • Pedro Resende
Verma modules. Irreducible representations obtained from Verma modules. This material followed sections 9.5 and 9.6 of Brian Hall's book.
11 Dezembro 2020, 11:00 • Pedro Resende
The tensor algebra of a vector space. The enveloping associative algebra of a Lie algebra. The Poincaré-Birkhoff-Witt theorem. Introduction to Verma modules. Exercise 7.13 of Brian Hall's book.
10 Dezembro 2020, 11:00 • Pedro Resende
Integral elements and dominant integral elements. Partial order on the set of integral elements. Basic properties. Integrality of the weights of the representations of semisimple Lie algebras, and invariance of the set of weights under the action of the Weyl group. Introduction to the theorem of the highest weight. This lecture was based on sections 8.7–8.8 and 9.1–9.2 of Brian Hall's book.
4 Dezembro 2020, 11:00 • Pedro Resende
Exercises from chapter 7 of Brian Hall's book: 1, 2, 4, 6, 9, 12.