Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2010 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 2010 • Question 7

Let \(G\) be a Lie group with Lie algebra \(\mathfrak {g}\). Given a subalgebra \(\mathfrak {h}\subseteq \mathfrak {g}\), prove there is a Lie subgroup \(H\le G\) whose Lie algebra is \(\mathfrak {h}\). (The entire proof with all details would be best. If not, then try to write the main ideas of the proof.)

Raw LaTeX

Let \(G\) be a Lie group with Lie algebra \(\mathfrak{g}\). Given a subalgebra
\(\mathfrak{h}\subseteq\mathfrak{g}\), prove there is a Lie subgroup \(H\le G\) whose
Lie algebra is \(\mathfrak{h}\). (The entire proof with all details would be best.
If not, then try to write the main ideas of the proof.)

Topic Tags

Lie Algebras and Exponential Maps Lie Groups and Matrix Lie Groups