# Tagged Questions

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### Is a finite depth-index irreducible subfactor, intermediate of a depth ≤ 3 one?

Let $(N \subset M)$ be a finite depth-index irreducible subfactor. Main question: Is $(N \subset M)$ the intermediate of a finite index depth $\le 3$ irreducible subfactor? (In others words, is ...
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### Are the integer index finite depth irreducible subfactors Kac-coideal?

Is it known whether or not the integer index finite depth irreducible subfactors (planar algebra) are Kac-coideal subfactors: $(R^{\mathbb{A}} \subset R^{\mathbb{I}})$, with $\mathbb{A}$ a finite ...
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### What are the first non-maximal non-group-subgroup simple irreducible subfactors?

Definition: For an irreducible (finite index) subfactor $(\mathcal{N} \subset \mathcal{M})$, an intermediate $(\mathcal{N} \subset \mathcal{P} \subset \mathcal{M})$ is normal if the biprojections ...
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### Are the finite dimensional von Neumann algebras, singly generated?

Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$ Question : Is it singly generated (as von Neumann algebra)? how ? ...
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### Are the reduced group Von Neumann algebra/ Group $C^{\ast}$ algebra functorial in the case of LCH groups

Let $G$ be a LCH group and $\mu$ be its left Haar measure. Call $\lambda_G : G \to U(L_2(G,\mu))$ the left regular representation. We can define the reduced $C^{\ast}$ algebra and reduced Von Neumann ...
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### The groupoid VN algebra of the transversal to a uniquely ergodic action

I have a uniquely ergodic dynamical system preserving a finite ergodic measure (specifically, I have a nice aperiodic tiling space with an action of $\mathbb{R}^d$). Thus the transformation group von ...
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### Question on structure of von Neumann algebras, clarification in Conway's “A course in operator theory”

I was reading the section on the structure of type I von Neumann algebras in John B. Conway's "A course in operator theory" and a few questions about certain definitions and references arose, I was ...
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### Reference request for a type III action of a group on a manifold

Let an action of a group $\Gamma$ on a manifold $M$ such that $L^{∞}(M)⋊Γ$ is a type $III$ factor. André Henriques posted here the following comment : I don't know the literature, so I can't ...
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### is this von Neumann algebra a tensor product?

Let $H_1$ and $H_2$ be Hilbert spaces. Let $A\subset B(H_1)$ be a factor and $A'$ its commutant. If a von Neumann algebra $M\subset B(H_1\otimes H_2)$ contains $A\otimes 1$ and commutes with ...
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### A non-hyperfinite type III factor from an action of the free group on the circle

We define below a von Neumann algebra $\mathcal{M}$ from an action of the free group on the circle, and we prove that $\mathcal{M}$ is a non-hyperfinite type III factor. Question : Is ...
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### Versions of the spectral theorem

Since any $C^*$-algebra can be represented as an algebra of bounded operators $\mathcal{B(H)}$ on a Hilbert space $\mathcal{H}$, the spectral theorem applies to all $C^*$-algebras: ($*$) ...
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### Folium in GNS construction and von Neumann algebras

The GNS construction allows one to represent a $C^*$-algebra as the algebra of bounded operators on a Hilbert space when a state is fixed, this state being represented as a vector on the Hilbert ...