Some prime factorization results for type II_1 factors

Abstract

We prove several unique prime factorization results for tensor products of type II_1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if $R\otimes L{F}_{r_1}\otimes ...\otimes L{F}_{r_m}$ is isomorphic to a subfactor in $R\otimes L{F}_{s_1}\otimes >...\otimes L{F}_{s_n}$, for some $2\le r_i,s_j\le \infty$, then $m\le n$.

Minor Adjustments

References in corpus (3)

• On a Class of Type II${}_1$ Factors with Betti Numbers Invariants
• Solid von Neumann Algebras
• On the Fundamental Group of Type II${}_1$ Factors

Cited by in corpus (43)

• On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups
• Unique prime factorization and bicentralizer problem for a class of type III factors
• Measure Equivalence Rigidity and Bi-exactness of Groups
• Complete descriptions of intermediate operator algebras by intermediate extensions of dynamical systems
• HNN Extensions of von Neumann Algebras
• Ideal bicombings for hyperbolic groups and applications
• W${}^{\ast }$-Rigidity for the von Neumann Algebras of Products of Hyperbolic Groups
• Rigidity of free product von Neumann algebras
• A Unique Prime Decomposition Result for Wreath Product Factors
• Inner amenability for groups and central sequences in factors
• Primeness results for von Neumann algebras associated with surface braid groups
• W*-rigidity paradigms for embeddings of II${}_1$ factors
• Some Applications of Group Theoretic Rips Constructions to the Classification of von Neumann Algebras
• Tensor product decompositions of II${}_1$ factors arising from extensions of amalgamated free product groups
• On fundamental groups of tensor product $\mathrm{I}{\mathrm{I}}_1$ factors
• Orbit equivalence rigidity for product actions
• Some estimates for non-microstates free entropy dimension, with applications to $q$-semicircular families
• Survey on geometric group theory
• Prime II${}_1$ factors arising from irreducible lattices in products of rank one simple Lie groups
• Finite Free Entropy and Free Group Factors
• Some prime factorization results for free quantum group factors
• Boundary Amenability of Relatively Hyperbolic Groups
• On the classification of inductive limits of II${}_1$ factors with spectral gap
• On Ozawa's Property for Free Group Factors
• Product rigidity in von Neumann and C${}^{\ast }$-algebras via s-malleable deformations
• Unique prime factorization for infinite tensor product factors
• A new construction of factors of type $\mathrm{II}{\mathrm{I}}_1$
• A Kurosh type theorem for type II_1 factors
• New examples of Property (T) factors with trivial fundamental group and unique prime factorization
• Weak Exactness for C*-algebras and Application to Condition (AO)
• On the Superrigidity of Malleable Actions with Spectral Gap
• The class S as an ME invariant
• $L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras
• Wreath-like products of groups and their von Neumann algebras I: $W^{\ast }$-superrigidity
• Classification of Tensor Decompositions of II${}_1$ Factors Associated With Poly-Hyperbolic Groups
• Generalized $q$-Gaussian von Neumann algebras with coefficients, III. Unique prime factorization results
• On cocycle actions of non-commutative Bernoulli shifts
• Classification results for nonsingular Bernoulli crossed products
• Ozawa's class $\mathcal{S}$ for locally compact groups and unique prime factorization
• Classification of tensor decompositions for II${}_1$ factors
• A Kurosh-Type Theorem for Type III Factors
• Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
• Strong primeness for equivalence relations arising from Zariski dense subgroups