Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2010 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 2010 • Question 6

Let \(U\) be a connected Lie subgroup of \(\mathrm {GL}_n(\mathbb {R})\). Suppose that every element of \(U\) has all of its entries below the main diagonal equal to 0, and all of its entries on the main diagonal equal to 1. Why is \(U\) diffeomorphic to \(\mathbb {R}^k\) for some \(k\)?

Raw LaTeX

Let \(U\) be a connected Lie subgroup of \(\GL_n(\R)\). Suppose that every
element of \(U\) has all of its entries below the main diagonal equal to 0, and all of
its entries on the main diagonal equal to 1. Why is \(U\) diffeomorphic to \(\R^k\) for
some \(k\)?

Topic Tags

Lie Groups and Matrix Lie Groups