Related papers: On intermediate subfactors of Goodman-de la Harpe-…
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…
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…
We survey results on Hedetniemi's conjecture which are connected to adjoint functors in the "thin" category of graphs, and expose the obstacles to extending these results.
We consider an intermediate factor situation in two categories: probability measure preserving ergodic theory and compact topological dynamics. In the first we prove a master-key theorem and examine a wide range of applications. In the…
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of…
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.
For a finite-index $\mathrm{II}_1$ subfactor $N \subset M$, we prove the existence of a universal Hopf $\ast$-algebra (or, a discrete quantum group in the analytic language) acting on $M$ in a trace-preserving fashion and fixing $N$…
We study actions of locally compact groups on von Neumann factors and the associated crossed-product von Neumann algebras. In the setting of totally disconnected groups we provide sufficient conditions on an action $G\curvearrowright Q$…
The Hanna Neumann conjecture gives a bound on the intersection of finitely generated subgroups of free groups. We explore a natural extension of this result, which turns out to be true only in the finite index case, and provide…
By using Ocneanu's result on the classification of all irreducible connections on the Dynkin diagrams, we show that the dual principal graphs as well as the fusion rules of bimodules arising from any Goodman-de la Harpe-Jones subfactors are…
Kinna--Wagner Principles state that every set can be mapped into some fixed iterated power set of an ordinal, and we write $\mathsf{KWP}$ to denote that there is some $\alpha$ for which this holds. The Kinna--Wagner Conjecture, formulated…
We review the framework subfactors provide for understanding modular invariants. We discuss the structure of a generalized Longo-Rehren subfactor and the relationship between the coupling matrices of such subfactors, modular invariance and…
We analyse the subgroup structure of direct products of groups. Earlier work on this topic has revealed that higher finiteness properties play a crucial role in determining which groups appear as subgroups of direct products of free groups…
Let $N \subset M$ be an irreducible inclusion of type type II$_1$ factors with finite Jones index. We shall introduce the notion of normality for intermediate subfactors of the inclusion $N \subset M$. If the depth of $N \subset M$ is 2,…
A hyperfinite $II_1$ subfactor may be obtained from a symmetric commuting square via iteration of the basic construction. For certain commuting squares constructed from Hadamard matrices, we describe this subfactor as a group-type inclusion…
A Krishnan-Sunder subfactor $R_U \ss R$ of index $k^2$ is constructed from a permutation biunitary matrix $U\in M_p(\mathbb{C})\otimes M_k(\mathbb{C})$, i.e. the entries of $U$ are either 0 or 1 and both $U$ and its block transpose are…
We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a…
If $N \subset P,Q \subset M$ are type II_1 factors with $N' \cap M = C id$ and $[M:N]$ finite we show that restrictions on the standard invariants of the elementary inclusions $N \subset P$, $N \subset Q$, $P \subset M$ and $Q \subset M$…
We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\Gamma < G= G_1 \times \dots \times G_d$ in higher rank semisimple algebraic…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.