3
votes
0answers
43 views

Discrete subgroups of SU(n) and SO(n).

Thank you very much for your concern. I am in physics background, any simpler but complete explanation would be helpful. I would like to know whether there is a complete understanding of discrete ...
0
votes
1answer
39 views

Projective linear group - solvable

Let $q\geq 5$ and let PGL(2,q) be the projective general linear group. Question Do there exists a $q$ such that PGL(2,q) is solvable?
2
votes
0answers
54 views

Lie Theory in Finite Groups

Currently, I have interest in Finite groups. I also want to learn Lie Groups, Lie algebras, and their representations. But I do not have any motivation for it. Question What are simple but ...
2
votes
1answer
33 views

How can I show that $ASL_n(F)$ is acting 2-transitively?

One of my friends asked me to ask this question here. This is a question from his last exam: Let $$ASL_n(F)=\{T_{A,v}:V_n(F)\to V_n(F)\mid\exists A\in SL_n(F), \exists v\in V_n(F), ...
0
votes
0answers
36 views

Smooth Action of a Finite Group

Suppose $H$ is a finite group acting smoothly on a smooth connected manifold $M$. The action is trivially proper, as $H$ is discrete. If the action of $H$ were also known to be free, i.e. $h\cdot ...
0
votes
0answers
70 views

The classification of irreducible representations of finite and compact Lie groups over $\mathbb{C}$

I just started reading a few lecture notes on representation theory and I was wondering about a big picture that one should keep in mind while reading through these lecture notes. Have all ...