Related papers: Fixed Point Algebras for Easy Quantum Groups

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 completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A. Kishimoto's result on the simplicity of such crossed products. We also give a…

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

We propose a definition of partition quantum spaces. They are given by universal $C^*$-algebras whose relations come from partitions of sets. We ask for the maximal compact matrix quantum group acting on them. We show how those fit into the…

We exhibit finitely generated torsion-free groups for which any action on any finite-dimensional CW-complex with finite Betti numbers has a global fixed point.

Suppose $A$ is a $C^*$-algebra and $H$ is a $C^*$-correspondence over $A$. If $H$ is regular in the sense that the left action of $A$ is faithful and is given by compact operators, then we compute the $K$-theory of $\mathcal{O}_A(H) \rtimes…

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…

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously…

We compute the $K$-groups for the Cuntz-Krieger algebras $\mathcal{O}_{A_{\mathcal{K}(f_{\mu})}}$, where $A_{\mathcal{K}(f_{\mu})}$ is the Markov transition matrix arising from the \textit{kneading sequence }$\mathcal{K} (f_{\mu})$ of the…

We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…

Let G be a connected, simply connected, simple complex algebraic group and let e be a primitive l-th root of 1, with l odd and 3 does not divide l if G is of type G_{2}. We determine all Hopf algebra quotients of the quantized coordinate…

We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure…

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C*-algebras. We prove the algebras generated by all shifts of a…

We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.

Let $\G$ be a group of type rotating automorphisms of an affine building $\cB$ of type $\wt A_2$. If $\G$ acts freely on the vertices of $\cB$ with finitely many orbits, and if $\Omega$ is the (maximal) boundary of $\cB$, then…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

We prove that for any automorphism $\alpha$ of a free group F of finite rank, one can efficiently compute a basis of the fixed point subgroup Fix(\alpha).

In this paper, we study the strong extension groups of Cuntz--Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz--Krieger algebra in the strong extension group and…

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…