Sumários
Lie groups and Lie algebras
9 Maio 2017, 17:00 • Susana Duarte Santos
Smooth distributions. Integrable and involutive distributions. The local and global Frobenius theorems. The one-to-one correspondence between the connected Lie subgroups of a Lie group and the Lie subalgebras of its Lie algebra. Connection between normal connected Lie subgroups of a connected Lie group and ideals of its Lie algebra.
Lie groups and Lie algebras
3 Maio 2017, 14:00 • Susana Duarte Santos
The exponential map of a Lie group: continuation of previous class. Surjectivity of the exponential map of GL(n,C).
Lie groups and Lie algebras
2 Maio 2017, 18:30 • Susana Duarte Santos
Resolution of exercises of the second chapter: 3, part of 4, part of 10, 11, 12, part of 13 and 20.
Lie groups and Lie algebras
2 Maio 2017, 17:00 • Susana Duarte Santos
The exponential map of a Lie group: main results. Examples.
Lie groups and Lie algebras
26 Abril 2017, 14:00 • Susana Duarte Santos
Integral curves, maximal integral curves and flows: definitions and main results for our purposes. Complete vector fields. Every left-invariant vector field on a Lie group is complete. One-parameter subgroups of a Lie group. Results and examples. The exponential map of a Lie group. Examples.