arXiv subjects

Sorin Popa

Publications and source records attributed to Sorin Popa.

59 records · Page 4Linked to original sources

arXiv2003

Some prime factorization results for type II_1 factors

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 $R \otimes LF_{r_1} \otimes ... \otimes LF_{r_m}$ is isomorphic to a subfactor in $R \otimes LF_{s_1} \otimes >... \otimes LF_{s_n}$, for some $2\leq r_i, s_j \leq \infty$, then $m\le n$.

math.OA↗

arXiv2003

On co-amenability for groups and von Neumann algebras

We first show that co-amenability does not pass to subgroups, answering a question asked by Eymard in 1972. We then address co-amenability for von Neumann algebras, describing notably how it relates to the former.

math.GR↗

arXiv2002

On the Fundamental Group of Type II$_1$ Factors

We present here a shorter version of the proof of a result from our paper ``On a class of type II$_1$ factors with Betti numbers invariants'', showing that the von Neumann factor associated with the group $\Bbb Z^2 \rtimes SL(2, \Bbb Z)$ has trivial fundamental group.

math.OA↗

arXiv1998

A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

Let $M$ be a factor with separable predual and $G$ a compact group of automorphisms of $M$ whose action is minimal, i.e. $M^{G^\prime}\cap M = C$, where $M^G$ denotes the $G$-fixed point subalgebra. Then every intemediate von Neumann algebra $M^G\subset N\subset M$ has the form $N=M^H$ for some closed subgroup $H$ of $G$. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions are made on the existence of a normal conditional expectation onto $N$.

funct-an↗

arXiv1998

Examples of subfactors with property T standard invariant

Let H and K be two finite groups with a properly outer action on the II_1 factor M. We prove that the group type inclusions $M^H \subset M \rtimes K$, studied earlier by Bisch and Haagerup, have property T in the sense of Popa if and only if the group generated by H and K in the outer automorphism group of M has Kazhdan's property T. This construction yields irreducible, infinite depth subfactors with small Jones indices and property T standard invariant.

math.OA↗