Questions tagged [noncompact]
The noncompact tag has no usage guidance.
9
questions
3
votes
1
answer
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Embed exceptional non-compact simply connected simple Lie groups into classical simple Lie groups with preserving centers
It is well known that there are exactly 22 exceptional simple real Lie algebras (5 compact, 5 split, 5 complex and 7 others). To each of these algebras there corresponds a unique simply connected (...
1
vote
1
answer
117
views
A neighborhood $Y$ of a set $X$ such that the line segment connecting any point in $Y$ and its projection to $X$ is contained in $Y$
A direct line from a point $p$ to a set $X$ is a line segment with one endpoint at $p$ and one endpoint in $X$, which is as short as any other line segment from $p$ to $X$. Given a closed set $X$ and ...
4
votes
0
answers
126
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Pushforward of invariant measures (equivariant Moser theorem)
There is a well-known theorem that between any two absolutely continuous Borel probability measures $\mu$ and $\nu$ on $\mathbb{R}^n$ there is an increasing triangular
transformation $T : \mathbb{R}^n ...
8
votes
1
answer
225
views
Measure support decomposition that "tends to infinity"
I would like to know the answers to the following two questions.
Let $S$ be a locally compact Hausdorff space, $\mu$ be a regular Borel measure with non-compact support $M$. Denote
$$
\mathscr{H}=\{\...
2
votes
1
answer
157
views
Li-Yorke chaos: the non compact case
1) Is there any notion of Li-Yorke chaos for non compact (metric) spaces $X$ and non continuous transformation $f:X \rightarrow X$? Could you bring some references?
2) I mean, why are so important ...
3
votes
0
answers
114
views
Extension of Schur-Weyl duality for principal series in $SL(2, \mathbb{R})$
In the case of $SU(N)$ all unitary irreps can be obtained from reducing tensor products ($V^{\otimes n}$) of the fundamental representation ($V$). Then given the set of all $SU(N)$ Young diagrams with ...
3
votes
1
answer
124
views
Totally minimal homeomorphisms on connected locally compact noncompact spaces
If $\alpha : X \to X$ is a minimal homeomorphism on a compact Hausdorff space $X$, then if $X$ is connected, $\alpha$ is totally minimal, that is $\alpha^k$ is minimal for every $k \in \mathbb{Z}$.
I ...
3
votes
1
answer
557
views
Compact dual of a noncompact Lie group
Let $\mathfrak{g}_0$ be a noncompact simple Lie algebra, and fix a Cartan involution $\theta$ of $\mathfrak{g}_0$, which gives a Cartan decomposition $\mathfrak{g}_0=\mathfrak{k}_0+\mathfrak{p}_0$. ...
2
votes
2
answers
307
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Unitary representations of SO(1,4) and SO(2,3)
Where can I find details about the irreducible unitary representations of SO(1,4) and SO(2,3)?