Sumários

Representations of simple Lie algebras

15 Dezembro 2020, 09:00 José António Maciel Natário

Fundamental weights and weight lattice. Weights of a representation. Highest weight. Alpha strings.


Classification of simple Lie algebras

14 Dezembro 2020, 12:00 José António Maciel Natário

Abstract root systems. Simple roots. Cartan matrix. Dynkin diagrams. Classification of simple Lie algebras.


Representations of Lie algebras (online)

7 Dezembro 2020, 12:00 José António Maciel Natário

Exponential map. Semisimple Lie algebras. Representations of Lie algebras. Adjoint representation. Killing form. Complexification and real forms. Cartan subalgebra. Roots.


Lie algebras and Lie groups (online)

30 Novembro 2020, 12:00 José António Maciel Natário

Lie algebras: definition and examples. Lie subalgebras, ideals, homomorphisms, isomorphism theorem. Lie groups: definition and examples. Lie algebra of a lie group.


Vectors and vector fields

24 Novembro 2020, 09:00 José António Maciel Natário

Tangent vectors and tangent bundle. Vector fields, Lie bracket.