Relative Property (T) Actions and Trivial Outer Automorphism Groups

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.

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。

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。

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。

Extension of automorphisms to C*-crossed products with non-trivial centre

Given a quasi-special endomorphism $ρ$ of a C*-algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by $ρ$. Exploiting some aspects of the underlying generalized Doplicher-Roberts duality theory based on Pimsner algebras, an obstruction to the existence of such extensions is found and described in terms of sections of a suitable group bundle.

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.

共轭 $\mathcal P(\mathbb N)/\mathrm{Fin}$ 的平凡自同构

Conjugating trivial automorphisms of $\mathcal P(\mathbb N)/\mathrm{Fin}$

本文研究 $\mathcal P(\mathbb N)/\mathrm{Fin}$ 的平凡自同构的共轭性，在连续统假设下给出无一阶和指标障碍的充要条件，并应用于证明粗空间的一致 Roe 冠状同构独立于 ZFC。

Notes on automorphisms of ultrapowers of II_1 factors

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II_1 factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is aleph_0-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II_1 factor, equality of the induced traces implies unitary equivalence. All statements are proved using operator algebraic techniques, but in the…