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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2016 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 2016 • Question 6

Let \(G\) be a Lie group with Lie algebra \(\mathfrak {g}\). If \(\mathfrak {h}\) is a subalgebra of \(\mathfrak {g}\), then prove there is a Lie subgroup \(H\le G\) whose Lie algebra is \(\mathfrak {h}\).

Raw LaTeX

Let \(G\) be a Lie group with Lie algebra \(\mathfrak{g}\). If \(\mathfrak{h}\) is
a subalgebra of \(\mathfrak{g}\), then prove there is a Lie subgroup \(H\le G\) whose
Lie algebra is \(\mathfrak{h}\).

Topic Tags

Lie Algebras and Exponential Maps Lie Groups and Matrix Lie Groups