Tagged Questions
0
votes
0answers
41 views
Is the Hilbert-Smith conjecture still unsolved?
Conjecture Let $G$ be a locally compact topological group. If $G$ has a continuous faithful group action on an $n$-manifold, then
$G$ is a Lie group.
Is this conjecture still unsolved? Is ...
1
vote
0answers
32 views
History: continuously differentiable groups over the real numbers
Continuously differentiable groups over the real numbers are all isomorphic to addition, as is well-known, but who proved it and when?
3
votes
1answer
128 views
Research Sources for $SL(2,R)$
Can anyone guide me to a good site for the special linear group $SL(2,R)$, especially one that goes deep into its subgroup and normal subgroup? Book recommendations would be great too.
10
votes
1answer
144 views
subgroup of connected locally compact group
I need a reference or a short proof for the following property:
A nontrivial connected locally compact group $G$ contains an infinite abelian subgroup.
0
votes
1answer
78 views
existence of infinite abelian subgroup in infinite locally compact groups
1) Let $G$ be an infinite locally compact group.
Does there exist an infinite abelian locally compact subgroup of $G$?
Rem: I know that there exists an infinite abelian subgroup in every infinite ...
1
vote
1answer
71 views
Centralizers in reductive Liegroups = unimodular?
Let $G$ be a real reductive group. Why is the centralizer of an element unimodular? What is a reference?
8
votes
2answers
291 views
Exact sequence in a nonabelian category [previously: “Exact sequence for topological groups?”]
If $A$, $B$, and $C$ are topological groups, and $f: A \to B$ and $g: B \to C$ are two continuous group homomorphisms, what does it usually mean for
$$1 \to A \stackrel{f}{\to} B \stackrel{g}{\to} C ...
4
votes
1answer
256 views
Completion of Topological Group with Metric
Related to this question, I'm having trouble understanding the construction of the completion of a topological group with metric structure. In particular, under what conditions is the completion also ...
