Related papers: Jones-Wassermann Subfactors for Disconnected Inter…
The representation theory of a conformal net is a unitary modular tensor category. It is captured by the bimodule category of the Jones-Wassermann subfactor. In this paper, we construct multi-interval Jones-Wassermann subfactors for unitary…
Motivated by our subfactor generalization of Wall's conjecture, in this paper we determine all intermediate subfactors for conformal subnets corresponding to four infinite series of conformal inclusions, and as a consequence we verify that…
An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard…
We describe the structure of the inclusions of factors A(E) contained in A(E')' associated with multi-intervals E of R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In…
We prove existence of subfactors of finite depth of the hyperfinite II_1 factor with indices (5+sqrt{13})/2= 4.302... and (5+sqrt{17})/2=4.561.... The existence of the former was announced by the second named author in 1993 and that of the…
We construct inclusions of the form $(B_0\otimes P)^G\subset (B_1\otimes P)^G$, where $G$ is a compact quantum group of Kac type acting on an inclusion of finite dimensional $\c^*$-algebras $B_0\subset B_1$ and on a $II_1$ factor $P$. Under…
We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These…
Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with…
A {\it W$^*$-representation} of a II$_1$ subfactor $N\subset M$ with finite Jones index, $[M:N]<\infty$, is a non-degenerate commuting square embedding of $N\subset M$ into an inclusion of atomic von Neumann algebras $\oplus_{i\in I} \Cal…
We consider noncommuting pairs P,Q of intermediate subfactors of an irreducible, finite-index inclusion N in M of II_1 factors such that P and Q are supertransitive with Jones index less than 4 over N. We show that up to isomorphism of the…
Given a subfactor planar algebra P, Guionnet, Jones and Shlyakhtenko give a diagrammatic construction of a II_{1} subfactor whose planar algebra is P. They showed if P is finite-depth, then the factors are interpolated free group factors,…
Subfactors of the hyperfinite II$_1$ factor with ''exotic'' properties can be constructed from nondegenerate commuting squares of multi-matrix algebras. We show that the subfactor planar algebra of these commuting square subfactors…
If $G$ is a countable, discrete group generated by two finite subgroups $H$ and $K$ and $P$ is a II$_1$ factor with an outer G-action, one can construct the group-type subfactor $P^H \subset P \rtimes K$ introduced in \cite{BH}. This…
We describe the subfactor planar algebra of an intermediate subfactor $N\subset Q \subset M$ of an extremal subfactor $N\subset M$ of finite Jones index which is not necessarily irreducible.
In this paper we consider a semigroup of completely positive maps $\tau=(\tau_t,t \ge 0)$ with a faithful normal invariant state $\phi$ on a type-$II_1$ factor $\cla_0$ and propose an index theory. We :achieve this via a more general…
Based on the fact that, for a subfactor $N$ of a II$_1$ factor $M,$ the first non-trivial Jones index is 2 and then $M$ is decomposed as the crossed product of $N$ by an outer action of ${\mathbb{Z}}_2,$ we study pairs $ \{N, uNu^* \}$ from…
To any complex Hadamard matrix H one associates a spin model commuting square, and therefore a hyperfinite subfactor. The standard invariant of this subfactor captures certain "group-like" symmetries of H. To gain some insight, we compute…
We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object…
This paper is the third of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we introduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtain…
We examine the notion of $\alpha$-strong singularity for subfactors of a \IIi factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its…