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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2017 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2017 • Question 5

Let \(G\) be a Lie group, and let \(H\) be the connected component of \(G\) that contains the identity. Prove that \(H\) is a Lie subgroup of \(G\), and that \(H\) is a normal subgroup of \(G\). (Do not use the theorem that closed subgroups of Lie groups are Lie groups.)

Raw LaTeX

Let \(G\) be a Lie group, and let \(H\) be the connected component of \(G\) that
contains the identity. Prove that \(H\) is a Lie subgroup of \(G\), and that \(H\) is a
normal subgroup of \(G\). (Do not use the theorem that closed subgroups of Lie
groups are Lie groups.)

Topic Tags

Lie Groups and Matrix Lie Groups