Related papers: Maximal von Neumann subalgebras arising from maxim…

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M. For $\alpha >0$, F is $\alpha$-bounded if the free packing $\alpha$-entropy of F is bounded from above. We say that M is strongly 1-bounded if M has a…

M.Newman has asked if it is the case that whenever H and K are isomorphic subgroups of a finite solvable group G with H maximal, then K is also maximal. This question was considered in a paper of I.M. Isaacs and the second author, where…

We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of…

We show that given a finitely generated LERF group $G$ with positive rank gradient, and finitely generated subgroups $A,B \leq G$ of infinite index, one can find a finite index subgroup $B_0$ of $B$ such that $[G : \langle A \cup B_0…

We provide an alternative proof for the extreme amenability of the unitary group of the hyperfinite II${}_1$-factor von Neumann algebra, endowed with the strong operator topology.

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

Consider a compact locally symmetric space $M$ of rank $r$, with fundamental group $\Gamma$. The von Neumann algebra $\vn(\Gamma)$ is the convolution algebra of functions $f\in\ell_2(\Gamma)$ which act by left convolution on…

We study the ISR (von Neumann invariant subalgebra rigidity) property for certain discrete groups arising as semidirect products from algebraic actions on certain 2-torsion groups, mostly arising as direct products of $\mathbb{Z}_2$. We…

Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\subset M$ that has infinite index under any projection in $Q'\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite Jones index). We prove that given any…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)\cap D\neq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of…

We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

Given an irreducible local conformal net A of von Neumann algebras on the circle and a finite-index conformal subnet B of A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu…

We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with uncountable fundamental groups and the…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We give necessary and sufficient conditions for which $\mathfrak A$ is…

Relationships between certain properties of maximal subalgebras of a Lie algebra $L$ and the structure of $L$ itself have been studied by a number of authors. Amongst the maximal subalgebras, however, some exert a greater influence on…

Let $M=M_1*M_2$ be a nontrivial tracial free product of finite von Neumann algebras. We prove that any amenable subalgebra of $M$ that has a diffuse intersection with $M_1$ is in fact contained in $M_1$. This has been proved by C. Houdayer…