The Calkin algebra has outer automorphisms

On Conjugacy of MASAs and the Outer Automorphism Group of the Cuntz Algebra

We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in O_n. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA D_n via Bogolubov automorphisms, that are not inner conjugate to D_n.

边界作用于索恩-汤普森群的外自同构群

Boundary actions of outer automorphism groups of Thompson-like groups

本文研究了索恩-汤普森群的外自同构群的边界作用，并证明这些群是C*-简单。

On Affine Orbifold Nets Associated with Outer Automorphisms

We construct solitons in affine orbifold nets associated with outer automorphisms, and we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to settle a number of questions concerning such orbifold constructions.

Every compact group arises as the outer automorphism group of a II_1 factor

We show that any compact group can be realized as the outer automorphism group of a factor of type II_1. This has been proved in the abelian case by Ioana, Peterson and Popa applying Popa's deformation/rigidity techniques to amalgamated free product von Neumann algebras. Our methods are a generalization of theirs.

具有最小外自同构群的 III$_1$ 型因子

A type III$_1$ factor with the smallest outer automorphism group

本文构造了一个具有可分预对偶的满的 III$_1$ 型因子，其外自同构群最小，即典范模同构嵌入是同构，方法为融合自由积。

Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism group

In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable fundamental group different from $\IRpos$. In fact, given any II$_1$ equivalence relation, we construct a II$_1$ factor with the same fundamental group. Given any locally compact unimodular second countable group $G$, our construction gives a II$_1$ equivalence relation $\RelR$ whose outer automorphism group is $G$. The same construction does not give a II$_1$ fa…

On the outer automorphism groups of triangular alternation limit algebras

Let $A$ denote the alternation limit algebra, studied by Hopenwasser and Power, and by Poon, which is the closed direct limit of upper triangular matrix algebras determined by refinement embeddings of multiplicity $r_k$ and standard embeddings of multiplicity $s_k$. It is shown that the quotient of the isometric automorphism group by the approximately inner automorphisms is the abelian group $ \ZZ ^d$ where $d$ is the number of primes that are divisors of infinitely many terms of each of the sequences $(r_k)$ and $(s_k)$. This group is also the group of automorphisms of the fundamental relatio…

Outer automorphism groups of some ergodic equivalence relations

Let R a be countable ergodic equivalence relation of type II_1 on a standard probability space (X,m). The group Out(R) of outer automorphisms of R consists of all invertible Borel measure preserving maps of the space which map R-classes to R-classes modulo those which preserve almost every R-class. We analyze the group Out(R) for relations R generated by actions of higher rank lattices, providing general conditions on finiteness and triviality of Out(R) and explicitly computing this group for the standard actions. The method is based on Zimmer's superrigidity for measurable cocycles, Ratner's …

关于某些图C*代数的外自同构

On outer automorphisms of certain graph $C^{*}$-algebras

本文构造了与可数交换群A同构的图C*代数，并展示了群的自同构如何提升为代数的自同构。

Relative Property (T) Actions and Trivial Outer Automorphism Groups

We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S.-Popa \cite[Def. 4.1]{Pop06}. There are uncountably many such actions up to orbit equivalence and von Neumann equivalence, and they may be chosen to be conjugate to any prescribed action when restricted to the free factors. We exhibit also, for every non-amenable free product of groups, free ergodic probability measure preserving actions whose associated equivalence relation has trivial outer automorphisms group. This gives in part…

每个局部紧群都是一个 II$_1$ 因子的外自同构群

Every locally compact group is the outer automorphism group of a II$_1$ factor

本文证明每个局部紧第二可数群都可实现为某个 II$_1$ 因子的外自同构群，方法是通过证明其为中心化子群，从而推广了此前仅适用于全不连通群和紧群的结果。

Trace scaling automorphisms of the stabilized Razak-Jacelon algebra

We classify trace scaling automorphisms of $\mathcal{W}\otimes\mathbb{K}$ up to outer conjugacy, where $\mathcal{W}$ is a certain simple separable nuclear stably projectionless C$^*$-algebra having trivial $K$-groups. Also, we show that all automorphisms of $\mathcal{W}$ with the Rohlin property are outer conjugate to each other. Moreover, we show that the central sequence C$^*$-algebra $F(\mathcal{W})$ of $\mathcal{W}$ is infinitee, which answers a question of Kirchberg.

Razak–Jacelon代数的非周期自同构

Aperiodic automorphisms of the Razak--Jacelon algebra

该研究分类了Razak–Jacelon代数的非周期自同构，引入了单可分单调迹C$^*$-代数自同构的弱稳定性概念，还探讨了无限型UHF代数与Jiang–Su代数的自同构。

Conjugate Pairs of Subfactors and Entropy for Automorphisms

Based on the fact that, for a subfactor $N$ of a II$_1$ factor $M,$ the first non-trivial Jones index is 2 and then $M$ is decomposed as the crossed product of $N$ by an outer action of ${\mathbb{Z}}_2,$ we study pairs $ \{N, uNu^* \}$ from a view point of entropy for two subalgebras of $M$ with a connection to the entropy for automorphisms, where the inclusion of II$_1$ factors $ N \subset M$ is given as $M$ is the crossed product of $N$ by a finite group of outer automorphisms and $u$ is a unitary in $M.$

Trace acaling automorphisms of certain stable AF algebras II

Two automorphisms of a simple stable AF algebra with a finite dimensional lattice of lower semicontinuous traces are shown to be outer conjugate if they act in the same way on the K-group and the extremal traces are scaled by numbers which are not equal to 1 and satisfy a certain condition (which always holds if all the scaling factors are less than 1). The proof goes via the Rohlin property. As an application we consider the problem of classifying conjugacy or outer conjugacy classes of certain actions of the circle group on a separable purely infinite C*-algebra.

A Dixmier type averaging property of automorphisms on a $C^*$-algebra

In his study of the relative Dixmier property for inclusions of von Neumann algebras and of $C^*$-algebras, Popa considered a certain property of automorphisms on $C^*$-algebras, that we here call the strong averaging property. In this note we characterize when an automorphism on a $C^*$-algebra has the strong averaging property. In particular, automorphisms on commutative $C^*$-algebras possess this property precisely when they are free. An automorphism on a unital separable simple $C^*$-algebra with at least one tracial state has the strong averaging property precisely when its extension to …

The Rohlin property for automorphisms of the Jiang-Su algebra

For projectionless C*-algebras absorbing the Jiang-Su algebra tensorially, we study a kind of the Rohlin property for autmorphisms. We show that the crossed products obtained by automorphisms with this Rohlin property also absorb the Jiang-Su algebra tensorially under a mild technical condition on the C*-algebras. In particular, for the Jiang-Su algebra we show the uniqueness up to outer conjugacy of the automorphism with this Rohlin property.

Automorphisms of free product-type and their crossed-products

A continuous family of non-outer conjugate aperiodic automorphisms whose crossed-products are all isomorphic is given on every interpolated free group factor. An explicit "duality" relationship between compact co-commutative Kac algebra (minimal) free product actions and free shift actions is also discussed.

Trace-scaling automorphisms of certain stable AF algebras

Trace scaling automorphisms of stable AF algebras with dimension group totally ordered are outer conjugate if the scaling factors are the same (not equal to one). This is an adaptation of a similar result for the AFD type II_infty factor by Connes and extends the previous result for stable UHF algebras.

群的 wreath 类积及其冯·诺依曼代数 II：外自同构

Wreath-like products of groups and their von Neumann algebras II: Outer automorphisms

针对群的冯·诺依曼代数外自同构问题，证实了琼斯关于一大类具卡扎德性质（T）的ICC群的猜想，并应用该结果证明对每个可数群$Q$，存在具性质（T）的ICC群$G$使其冯·诺依曼代数外自同构群同构于$Q$。