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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2019 • Question 2

Question

Math 6510 • Differentiable Manifolds Spring 2019 • Question 2

Find all connected Lie subgroups of \(\mathrm {SL}_2(\mathbb {R})\) that contains the subgroup \[ H= \left \{ \begin {pmatrix} 1 & x\\ 0 & 1 \end {pmatrix} : x\in \mathbb {R} \right \}. \]

Raw LaTeX

Find all connected Lie subgroups of \(\mathrm{SL}_2(\R)\) that contains the
subgroup
\[
  H=
  \left\{
    \begin{pmatrix}
      1 & x\\
      0 & 1
    \end{pmatrix}
    : x\in\R
  \right\}.
\]

Topic Tags

Fundamental Groups Lie Groups and Matrix Lie Groups