Related papers: Poly-$\mathbb{Z}$ group actions on Kirchberg algeb…

This is the second part of our serial work on the classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of…

We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unitary tensor categories on Kirchberg algebras. In particular,…

We prove that every action of a finite group all of whose Sylow subgroups are cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the Kirchberg algebra. The proof uses a construction of Kirchberg algebras…

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…

We classify a large class of Z^2-actions on the Kirchberg algebras employing the Kasparov group KK^1 as the space of classification invariants.

We show an equivariant Kirchberg-Phillips-type absorption theorem for pointwise outer actions of discrete amenable groups on Kirchberg algebras with respect to natural model actions on the Cuntz algebras $\mathcal{O}_\infty$ and…

We give a complete classification up to cocycle conjugacy of uniformly outer actions of Z^2 on UHF algebras. In particular, it is shown that any two uniformly outer actions of Z^2 on a UHF algebra of infinite type are cocycle conjugate. We…

Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra…

We classify the (filtered) Hopf actions of Hopf-Ore extensions of group algebras on path algebras of quivers, extending results in several other works from special cases to this general setting. Having done this for general Hopf-Ore…

In this article, we investigate Hopf actions on vertex algebras. Our first main result is that every finite-dimensional Hopf algebra that inner faithfully acts on a given \pi_2-injective vertex algebra must be a group algebra. Secondly,…

We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel-Thomas) twists and are reminiscent of the Rickard complexes…

We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebra has the structure of a generalized cluster algebra. This…

Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner…

The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is…

We introduce a hierarchy for unital Kirchberg algebras with finitely generated K-groups by which the first and second homotopy groups of the automorphism groups serve as a complete invariant of classification. We also introduce an invariant…

Quasi-free actions of finite groups on Cuntz algebras $\mathcal O_n$ for $n\geq 2$ are classified up to conjugacy by data in the representation ring. Partial results are obtained for quasi-free actions by compact groups.

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two…

We prove that all strongly outer Z^N-actions on a UHF algebra of infinite type are strongly cocycle conjugate to each other. We also prove that all strongly outer, asymptotically representable Z^N-actions on a unital simple AH algebra with…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.