Related papers: Commuting-Square Subfactors and Central Sequences

We show that if $A$ is a separable, simple and non-type I C$^{\ast}$ algebra, then for every properly infinite hyperfinite von Neumann algebra $M$ with separable predual, its Ocneanu ultrapower $M'\cap M^{\omega}$ arises as a sub-quotient…

We construct two infinite series of Moufang loops of exponent $3$ whose commutative center (i.e. the set of elements that commute with all elements of the loop) is not a normal subloop. In particular, we obtain examples of such loops of…

We construct irreducible hyperfinite subfactors of index 6 with a prescribed fundamental group from a large family containing all countable and many uncountable subgroups of R_+. We also prove that there are unclassifiably many irreducible…

A quadrilateral of factors is an irreducible inclusion of factors $N \subset M$ with intermediate subfactors $P$ and $Q$ such that $P$ and $Q$ generate $M$ and the intersection of $P$ and $Q$ is $N$. We investigate the structure of 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 $Q \subset M$…

Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar…

Given a II$_1$ factor $M$, a W$^*$-subalgebra $Q\subset M$ is {\it compressible} if for any $\varepsilon>0$ there exists a finite set of unitary elements $\Cal U_0\subset \Cal U(M)$ such that $\| \frac{1}{|\Cal U_0|}\sum_{u\in \Cal U_0}…

The relative commutant $A'\cap A^{\mathcal{U}}$ of a strongly self-absorbing algebra $A$ is indistinguishable from its ultrapower $A^{\mathcal{U}}$. This applies both to the case when $A$ is the hyperfinite II$_1$ factor and to the case…

For any finite dimensional C*-algebra A with any trace vector {\vec s} whose components are rational numbers, we give an endomorphism {\Phi} of the hyperfinite II_1 factor R such that: forall k in {\mathbb N} {\Phi}^k (R)' \cap R= \otimes^k…

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 show that any infinite ring has an infinite nonunital compressed commuting graph. We classify all infinite unital rings with finite unital compressed commuting graph, using semidirect product of rings as our main tool. As a consequence…

A finite non-abelian group $G$ is called commuting integral if the commuting graph of $G$ is integral. In this paper, we show that a finite group is commuting integral if its central factor is isomorphic to ${\mathbb{Z}}_p \times…

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 show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb{C})$ admits an orthonormal unitary…

We construct numerous continuous families of irreducible subfactors of the hyperfinite II$_1$ factor, which are non-isomorphic, but have all the same standard invariant. In particular, we obtain 1-parameter families of irreducible,…

We give sufficient conditions, in terms of the existence of unbounded derivations satisfying certain properties, which ensure that a II$_1$ factor $M$ is prime or has at most one Cartan subalgebra. For instance, we prove that if there…

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 show that, given a continuous action $\alpha$ of a locally compact group $G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_{\alpha} G)$ is contained in $M\rtimes_{\alpha} H$ where $H$ is the subgroup of elements acting without…

We give a subfactor construction for a $II_{1}$ factor M which is not anti-isomorphic to itself. The $II_{1}$ factor we consider is essentially the same as the example previously given by Connes. However, our construction uses the recently…

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided…