Related papers: On Pimsner Popa bases

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…

Let M be a factor of type III with separable predual and with normal states phi_1,...,phi_k, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is shown that there is a unitary operator u in M such that…

We show that if a finite dimensional Hopf algebra over ${\bf C}$ has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group $G$ and a factorization $G=G_+G_-$ into two…

For real factors the notions of the coupling constant and the index are introduced and investigated. The possible values of the index for type II$_1$ real factors are calculated, in a similar way as for the complex case.

Guionnet et al. gave a construction of a II_1 factor associated to a subfactor planar algebra. In this paper we define an unshaded planar algebra. To any unshaded planar algebra P we associate a finite von Neumann algebra M_P. We prove that…

We study several model-theoretic aspects of W$^*$-probability spaces, that is, $\sigma$-finite von Neumann algebras equipped with a faithful normal state. We first study the existentially closed W$^*$-spaces and prove several structural…

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

Jones proposed the study of two subfactors of a $II_1$ factor as a quantization of two closed subspaces in a Hilbert space. The Pimsner-Popa probabilistic constant, Sano-Watatani angle, interior and exterior angle, and Connes-St{\o}rmer…

This paper studies weakly mixing (singular) and mixing masas in type $\rm{II}_{1}$ factors from a bimodule point of view. Several necessary and sufficient conditions to characterize the normalizing algebra of a masa are presented. We also…

Popa introduced the tensor category $\tilde{\chi}(M)$ of approximately inner, centrally trivial bimodules of a $\rm{II}_{1}$ factor $M$, generalizing Connes' $\chi(M)$. We extend Popa's notions to define the $\rm W^*$-tensor category…

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…

We introduce the notion of a generalized Jung factor: a II$_1$ factor $M$ for which any two embeddings of $M$ into its ultrapower $M^{\mathcal U}$ are equivalent by an automorphism of $M^{\mathcal U}$. We show that $\mathcal R$ is not the…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…

We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II_1 factors and their ultrapowers. Among other things, we show that for any II_1 factor M, there are continuum many nonisomorphic…

This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are…

We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…

We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise…

We call a subfactor trivial if it is isomorphic with the obvious inclusion of N into matrices over N. We prove the existence of type II_1 factors M without non-trivial finite index subfactors. Equivalently, every M-M-bimodule with finite…

Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a…