Sumários
Lie groups and Lie algebras
4 Abril 2017, 17:00 • Susana Duarte Santos
The complexification of a real Lie algebra.
Tangent bundle of a manifold M, rough and smooth vector fields on M, derivations on C∞(M): examples. Lie brackets of smooth vector fields. Results and properties. Related smooth vector fields: results, properties and examples. The pushforward of a smooth vector field by a diffeomorphism.
Lie groups and Lie algebras
29 Março 2017, 14:00 • Susana Duarte Santos
Direct product of two Lie algebras. Quotient of a Lie algebra by a Lie ideal. Lie algebra homomorphisms. Examples. First isomorphism theorem. Examples. Representations of a Lie algebra and Ado's theorem. The adjoint representation of a Lie algebra. Derivations of an algebra. The inner derivations of a Lie algebra: properties. Structure constants.
Lie groups and Lie algebras
28 Março 2017, 18:30 • Susana Duarte Santos
Examples related to the theory already developed.
Lie groups and Lie algebras
28 Março 2017, 17:00 • Susana Duarte Santos
More results about Lie group homomorphisms. One more example of Lie subgroups: a dense Lie subgroup of the 2-torus.
Lie algebra: definition, examples and properties. Lie subalgebras and Lie ideals of a Lie algebra: examples. The center and the derived algebra of a Lie algebra. Simple Lie algebras: examples.
Lie groups and Lie algebras
22 Março 2017, 14:00 • Susana Duarte Santos
Lie group homomorphisms and Lie group isomorphisms: properties and examples. Quaternions. Some examples of isomorphic Lie groups.