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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2021 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 2021 • Question 6

Let \(\phi : G \to H\) be a Lie group homomorphism between Lie groups \(G\) and \(H\). Let \(X\) and \(Y\) be \(\phi \)-related vectors fields on \(G\) and \(H\), respectively, and assume that \(Y\) is left invariant. Is \(X\) left invariant? Either prove this or provide a counterexample.

Raw LaTeX

Let \(\phi : G \to H\) be a Lie group homomorphism between Lie groups
\(G\) and \(H\). Let \(X\) and \(Y\) be \(\phi\)-related vectors fields on \(G\) and \(H\),
respectively, and assume that \(Y\) is left invariant. Is \(X\) left invariant?
Either prove this or provide a counterexample.

Topic Tags

Left-Invariant Vector Fields Lie Group Actions and Homomorphisms Lie Groups and Matrix Lie Groups Vector Fields and Flows