2
votes
1answer
157 views

left-invariant n-form and metric on a Lie group

These two questions are from my exam practice question sets , which are quite similar. I got some problem understanding and solving both of them . For (a) , I can only substite $dx\wedge dy\wedge ...
0
votes
1answer
67 views

Lie bracket of vector fields on $\Bbb R^{n}$

Please show how to solve? I am stack with lie bracket. Thank you.
8
votes
4answers
330 views

Determining the action of the operator $D\left(z, \frac d{dz}\right)$

This question was motivated by a question by Tobias Kienzler and its wonderful answers. I begin as in the linked question... Using the Taylor expansion $$f(z+a) = \sum_{k=0}^\infty ...
0
votes
1answer
244 views

Lie algebra of the bounded continuous functions

I can think of the set of bounded, continuous functions from $\mathbb R \to \mathbb R$ as a group, with composition as addition of functions. In other words, this group has the rule that the ...