Related papers: Rokhlin dimension for compact quantum group action…

We show that for any locally compact Hausdorff space $Y$ with finite covering dimension and for any continuous flow $\mathbb{R} \curvearrowright Y$, the resulting crossed product $C^*$-algebra $C_0(Y) \rtimes \mathbb{R}$ has finite nuclear…

In this paper, we show that one of the conditions in the definition of weak tracial Rokhlin property for finite group actions on simple unital C*-algebras can be replaced by a seemingly weaker condition, or a seemingly stronger condition.…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

We introduce the notion of the weak tracial approximate representability of a discrete group action on a unital $C^*$-algebra which could have no projections like the Jiang-Su algebra $\mathcal{Z}$. Then we show a duality between the weak…

We construct new examples of inclusions of unital $C\sp*$-algebras of index-finite type with the Rokhlin property motivated by a broader attempt to understand the range of such inclusions beyond known models. In the course of this…

Tracial Rokhlin property was introduced by Phillips to prove various structure theorems for crossed product. But it is defined for actions on simple C*-algebras only. This paper consists of two major parts: In section 2 and 3, we study the…

In this paper we will introduce the tracial Rokhlin property for an inclusion of separable simple unital C*-algebras $P \subset A$ with finite index in the sense of Watatani, and prove theorems of the following type. Suppose that $A$…

In this paper, we introduce compact group actions with the weak tracial Rokhlin property. This concept simultaneously generalizes finite group actions with the weak tracial Rokhlin property and compact group actions with the tracial Rokhlin…

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning actions of locally compact quantum groups on C*-algebras [S. Baaj, G. Skandalis and S. Vaes, 2003]. Let $\cal G$ be…

We introduce the Rohlin property and the approximate representability for finite group actions on stably projectionless C*-algebras and study their basic properties. We give some examples of finite group actions on the Razak-Jacelon algebra…

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of…

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful…

We characterise when the C*-algebra C*(G) of a locally compact and Hausdorff groupoid G is subhomogeneous, that is, when its irreducible representations have bounded finite dimension; if so we establish a bound for its nuclear dimension in…

We establish finite nuclear dimension for crossed product C*-algebras arising from various classes of possibly non-free topological actions, including arbitrary actions of finitely generated virtually nilpotent groups on finite dimensional…

We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

We show that for any countable discrete maximally almost periodic group $G$ and any UHF algebra $A$, there exists a strongly outer product type action $\alpha$ of $G$ on $A$. We also show the existence of countable discrete almost abelian…

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations…

We shall introduce the approximate representability and the Rohlin property for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra and discuss some basic properties of approximately representable coactions and…

We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite generator theorem and use it to establish…