On C*-algebras Associated with Sofic Shifts
Toke Meier Carlsen
证明了对于sofic移位λ，Matsumoto的C* 代数-代数O_Lambda同构于λ的左Krieger覆盖图的Cuntz-Krieger代数.
We show that for a sofic shift Lambda, Matsumoto's C*-algebra O_Lambda is isomorphic to the Cuntz-Krieger algebra of the left Krieger cover graph of Lambda.
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On the Structure of Covers of Sofic Shifts
引入了一个将左Fischer覆盖推广到任意sofic移位的典型覆盖，并证明了sofic移位的左Krieger覆盖和过去集覆盖可以划分为自然层.这些结果被用来寻找流不变量的值域和研究与sofic移位空间相关联的泛C*-代数的理想结构。
Entropy and the variational principle for actions of sofic groups
最近Lewis Bowen在容许有限熵生成划分的标准概率空间上引入了可数sofic群的保测度作用的熵概念。通过应用算子代数的角度来看，我们开发了一个更一般的方法，sofic熵产生测量和拓扑动力学不变量，我们建立了变分原理在这方面。在剩余有限群的情况下，利用变分原理计算了定义群环元在完全群C*-代数中可逆的主代数作用的拓扑熵.
We give an alternate proof of a Theorem of Elek and Szabo establishing Lück's determinant conjecture for sofic groups. Our proof is based on traces on group C*-algebras. We briefly discuss the relation with Atiyah's problem on the integrality of $L^2$-Betti numbers.
Reducibility of Covers of AFT shifts
本文证明了sofic移位的几个覆盖的约化结构是流不变量。此外，我们还证明了对于几乎有限型的不可约子移位，左Krieger覆盖和过去集覆盖是可约的。给出了一个例子，证明了存在具有可约左Krieger覆盖的非几乎有限型移位。作为应用，我们证明了几乎有限型不可约严格sofic移位的Matsumoto代数不是简单的。
We show that if $Γ$ is an infinite finitely generated finitely presented sofic group with zero first $L^{2}$ Betti number then the von Neumann algebra $L(Γ)$ is strongly $1$-bounded in the sense of Jung. In particular, $L(Γ)\not\cong L(Λ)$ if $Λ$ is any group with free entropy dimension $>1$, for example a free group. The key technical result is a short proof of an estimate of Jung using non-microstates entropy techniques.
Associated to any orthogonal representation of a countable discrete group is an probability measure-preserving action called the Gaussian action. Using the Polish model formalism we developed before, we compute the entropy (in the sense of Bowen, Kerr-Li) of Gaussian actions when the group is sofic. Computations of entropy for Gaussian actions has only been done when the acting group is abelian and thus our results are new even in the amenable case. Fundamental to our approach are methods of noncommutative harmonic analysis and $C^{*}$-algebras which replace the Fourier analysis used in the ab…
The class of normal subshifts includes irreducible infinite topological Markov shifts, irreducible infinite sofic shifts, synchronized systems, Dyck shifts, $β$-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated $C^*$-algebras and its gauge actions with potentials.
C*-algebras of labelled graphs
本文描述了一类$C^*$ -代数，它同时推广了Tomforde的超图代数和Matsumoto的移位空间$C^*$ -代数.在这样做的时候，我们揭示了一些新的光不同的$C^*$ -代数，可能与一个移位空间。最后，我们展示了如何将一个简单的$C^*$ -代数与一个不可约sofic移位相关联。
Synchronizing Dynamical Systems: Shift Spaces and $K$-Theory
本文针对同步移位空间，基于Bratteli图构建了同宿、异宿及同步异宿$C^*$-代数与同步理想，详细计算了偶移位等例子的不变量，并探讨了同宿代数$K$-理论秩的意义及从极小移位构造同步移位的方法。
We will introduce a notion of normal subshifts. A subshift $(Λ,σ)$ is said to be normal if it satisfies a certain synchronizing property called $λ$-synchronizing and is infinite as a set. We have lots of purely infinite simple $C^*$-algebras from normal subshifts including irreducible infinite sofic shifts, Dyck shifts, $β$-shifts, and so on. Eventual conjugacy of one-sided normal subshifts and topological conjugacy of two-sided normal subshifts are characterized in terms of the associated $C^*$-algebras and the associated stabilized $C^*$-algebras with its diagonals and gauge actions, respect…
Pushdown automata, lambda-graph systems and C*-algebras
一个$λ$ -图系统是一个带有某种附加结构的标号Bratteli图，它表示一个子移位并产生一个$C^*$ -代数.本文从下推自动机出发构造了一个$λ$ -图系统，使得该自动机所接受的语言与$λ$ -图系统所给出的子移位的可接受词的语言一致.给出了接受Markov-Dyck移位和sofic-Dyck移位语言的下推自动机的$λ$ -图系统。
Vanishing first cohomology and strong 1-boundedness for von Neumann algebras
本文简化证明了sofic有限表示群若一阶ℓ²-Betti数消失则其群冯·诺依曼代数是强1有界的，并给出性质T情形的简短证明。
Textile systems on lambda-graph systems
子移位的符号矩阵系统和$λ$ -图系统的概念分别是符号矩阵和$λ$ -图（=有限符号矩阵）的推广（[Doc. 4（1999），285-340]）。M. Nasu为了研究拓扑Markov移位的自同构和自同态，引入了图同态对的织纹系统的概念（[Mem.Amer.Math.Soc.546，114（1995）]）。在这篇文章中，我们在$λ$ -图系统上构造了纺织系统，并研究了子移位上的自同构。我们将证明，对于一个子移位$(Λ,σ)$的前向自同构$ϕ$，自同构$ϕ^k σ^n, k\ge 0, n\ge 1$可以明确地实现为一个子移位定义的某些符号矩阵系统来自表示$ϕ$的强移位等价和子移位$(Λ,σ)$。作为该结果的应用，如果子移位$Λ$的自同构$ϕ$是简单自同构，则动力系统$(Λ, ϕ\circ σ)$与子移位$(Λ, σ).$拓扑共轭
We study strong compactly aligned product systems of $\mathbb{Z}_+^N$ over a C*-algebra $A$. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of $A$. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite). Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher ra…
To every one-sided shift space $\mathsf{X}$ we associate a cover $\tilde{\mathsf{X}}$, a groupoid $\mathcal{G}_{\mathsf{X}}$ and a $\mathrm{C^*}$-algebra $\mathcal{O}_{\mathsf{X}}$. We characterize one-sided conjugacy, eventual conjugacy and (stabilizer preserving) continuous orbit equivalence between $\mathsf{X}$ and $\mathsf{Y}$ in terms of isomorphism of $\mathcal{G}_{\mathsf{X}}$ and $\mathcal{G}_{\mathsf{Y}}$, and diagonal preserving $^*$-isomorphism of $\mathcal{O}_{\mathsf{X}}$ and $\mathcal{O}_{\mathsf{Y}}$. We also characterize two-sided conjugacy and flow equivalence of the associate…
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