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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2017 • Question 4

Question

Math 6510 • Differentiable Manifolds Spring 2017 • Question 4

Let \(G\) be a connected Lie group with Lie algebra \(\mathfrak {g}\) such that \([X,Y]=0\) for all \(X,Y\in \mathfrak {g}\). Prove that \(G\) is abelian.

Raw LaTeX

Let \(G\) be a connected Lie group with Lie algebra \(\mathfrak{g}\) such that
\([X,Y]=0\) for all \(X,Y\in\mathfrak{g}\). Prove that \(G\) is abelian.

Topic Tags

Lie Algebras and Exponential Maps Lie Groups and Matrix Lie Groups