All Questions
Tagged with von-neumann-algebras rt.representation-theory
12 questions
2
votes
0
answers
145
views
About normal states in abstract von Neumann algebras
In the book "Fundamental of the theory of operator algebras" (KAdisong and Ringrose, Vol 2) we have the Corollary 7.1.16
but this was state only for concrete von Neumann algebras (because ...
- 424
3
votes
1
answer
285
views
Extreme points of the set of all traces
Let $G$ be a finitely generated group with a bound on its complex unitary irreducible representations: That is assume all complex unitary irreducibles of $G$ have degrees at most $k$ for some integer $...
- 193
5
votes
1
answer
341
views
The center of a representation von Neumann algebra, and finite index subgroups
Consider a (countable) group $G$, a subgroup $H\leq G$ of finite index, and a unitary representation $\pi:G\to \mathcal{U}(\mathcal{H})$.
If the center of the von Neumann algebra $\pi(H)''$ is finite ...
4
votes
1
answer
357
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Families of representations of von Neumann algebras
Let $A$ be a von Neumann algebra and let $H$ be a (separable) Hilbert space.
It is known (see e.g., Section IV, Thm. 5.5 of Takesaki I) that there exists a Hilbert space $K$ such that $A \subset \...
- 9,853
31
votes
0
answers
919
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Is this representation of Go (game) irreducible?
This post is freely inspired by the basic rules of Go (game), usually played on a $19 \times 19$ grid graph.
Consider the $\mathbb{Z}^2$ grid. We can assign to each vertex a state "black" ($b$), "...
3
votes
0
answers
141
views
Existence of a unique cyclic and separating vector in a *-representation
I'm interested in knowing the requirements for a $*$-representation, $\pi_{\omega}$, of a C*-algebra, $\mathbb{C}(\mathcal{G})$, (or equivalently the requirements for the unitary representation, $U_{\...
- 31
4
votes
1
answer
325
views
Do irreducible characters form a closed set?
A character on a discrete group $\Gamma$ is a conjugation-invariant function $\tau$ which is of positive
type, and is normalized so that $\tau(e) = 1$, where $e$ is the identity element of $\Gamma$. A ...
- 1,418
3
votes
0
answers
98
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Quantum Groups and quantum spaces - From algebra to Analysis
My question will be about the non-standard quantum projective space $\mathcal{A}_q(\mathbb{CP}^n(c,d))$ introduced by Dijkhuizen and Noumi. I want to see this algebra now on a von Neumann algebraic ...
8
votes
1
answer
422
views
The positive cone of the standard representation of a Von Neumann algebra
Let $A$ be a von Neumann algebra, let $L^2(A)$ be the underlying Hilbert space of the standard form of $A$, and $P \subset L^2(A)$ the canonical positive cone (see for example this paper by Haagerup). ...
- 42.4k
5
votes
0
answers
428
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Koopman representation, weakly compact action, Ozawa Popa
Given a weakly compact action (Ozawa-Popa) of a discrete group $\Gamma$ on p.m space $X$, consider the Koopman representation $\pi$ on $L^2(X)$. Compose this representation with the Calkin projection. ...
- 193
7
votes
1
answer
561
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How does the right regular of GL(n, R) and GL(n,Qp) decompose?
The question is contained in the title. I would guess that this question is already answered in the literature.
Given the reductive group $GL(n)$ over a complete local field, how does the right ...
- 11.2k
18
votes
0
answers
895
views
local equivalence of loop group representations
Let $G$ be a compact, simple, connected, simply connected (cscsc) Lie group, and let its smooth loop group $LG:=C^\infty(S^1,G)$. Given an interval $I\subset S^1$, we have the local loop group
$$
L_IG ...
- 43.2k