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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2013 • Question 1

Question

Math 6510 • Differentiable Manifolds Spring 2013 • Question 1

Let \(A\) be an element of the Lie algebra of \(\mathrm {GL}_n(\mathbb {R})\). What is the left-invariant vector field on \(\mathrm {GL}_n(\mathbb {R})\) that is associated to \(A\)? Show that it is left-invariant.

Raw LaTeX

Let \(A\) be an element of the Lie algebra of \(\GL_n(\R)\). What is the
left-invariant vector field on \(\GL_n(\R)\) that is associated to \(A\)? Show that
it is left-invariant.

Topic Tags

Left-Invariant Vector Fields Lie Algebras and Exponential Maps Lie Groups and Matrix Lie Groups Vector Fields and Flows