# Tagged Questions

**14**

votes

**3**answers

1k views

### What's a noncommutative set?

This issue is for logicians and operator algebraists (but also for anyone who is interested).
Let's start by short reminders on von Neumann algebra (for more details, see [J], [T], [W]):
Let $H$ ...

**7**

votes

**0**answers

270 views

### Canonical Time Evolution for Type $II_{1}$-Factors?

This question was spurred by the answer of Steve Huntsman to the MO question here. The Tomita-Takesaki modular automorphism group gives rise to a canonical time evolution on a type $III$ factor ...

**5**

votes

**2**answers

693 views

### Universal characterization and explicit description of elements of the group von Neumann algebra and the crossed product

Group von Neumann algebras and crossed products for a locally compact group G
can be constructed in many different ways.
For example, one can take the von Neumann algebra generated
by certain ...

**13**

votes

**3**answers

1k views

### Is the group von Neumann algebra construction functorial?

Let $G$ be a group and $CG$ the complex group algebra over the field $C$ of complex number. The group von Neumann algebra $NG$ is the completion of $CG$ wrt weak operator norm in $B(l^2(G))$, the set ...

**7**

votes

**3**answers

1k views

### Definition of a von Neumann algebra

Is there a way to equip every C*-algebra A with a functorial topology such that
the canonical map A→A** is an isomorphism if and only if A is a von Neumann algebra?
Here A** denotes the dual of A* in ...

**4**

votes

**1**answer

260 views

### One-parameter semigroups of bimodules

Suppose M is a von Neumann algebra.
Consider a monoidal category of bimodules over M.
Here a bimodule is a Hilbert space with two normal representations of M.
The monoidal structure is given by ...

**11**

votes

**5**answers

2k views

### Non-commutative geometry from von Neumann algebras?

The Gelfand transform gives an equivalence of categories from the category of unital, commutative $C^*$-algebras with unital $*$-homomorphisms to the category of compact Hausdorff spaces with ...

**8**

votes

**1**answer

376 views

### Maximal localizations of von Neumann algebras

Suppose M is a von Neumann algebra.
Denote by L its maximal noncommutative localization,
i.e., the Ore localization with respect to the set of all left and right regular elements,
i.e., elements whose ...