Homework 4 Problem 1

Problem 1

Do there exist nonorientable Lie groups? If so, give an example. If not, why not?

Solution

All Lie groups are orientable. I can illustrate this by example. A Lie group acting on a form is like translation. The pull back of the translation doesn't change the sign of the form. Hence, the Lie group is orientable.

Discussion

I realize this argument is weak, but then so is my understanding of geometry. Any feedback is appreciated.

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