Keisuke Yoshida
We characterize the simplicity of universal C$^*$-algebras arising from multispinal groups. Let $\mathcal{O}_{G_{\max}}$ be the universal C$^*$-algebra associated to a multispinal group $G$. We show that the invertibility of a matrix completely determines the simplicity of $\mathcal{O}_{G_{\max}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Simplicity of $*$-algebras of non-Hausdorff $\mathbb{Z}_2$-multispinal groupoids
本文研究 $\mathbb{Z}_2$-多脊柱型自相似群产生的 $C^*$-代数的单性，通过识别一类无限 $2$-设计族给出 Steinberg 代数单性的充分条件，并进而证明相应 $C^*$-代数的单性，推广了 Grigorchuk 情形下的既有结果。
Simplicity of algebras and $C^*$-algebras of self-similar groupoids
通过逆半群代数刻画自相似群胚的Steinberg代数的单性，并证明收缩自相似群胚的约化$C^*$-代数与Steinberg代数的单性一致。
Simplicity of $C^*$-algebras of contracting self-similar groups
本文证明了收缩自相似群对应的$C^*$-代数与复$\t$-代数单性等价，并改进了判定算法，为充足群胚提供了新实例。
Let (G,S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C-*-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C>0 and a natural number L such that for a function f in l^2(G) supported on elements of length n with respect to the generating set S: || f * h || <= C(n+1)^{3/2 L} || f || || h ||, forall h in l^2(G).
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently obtained by the second and third named authors. In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to take the study of C*-simplicity a step further, and in addition to settle the longstanding open problem of characterizing groups with the unique trace property. We give a new and self-contained proof of …
Simplicity of action-based $C^{*}$-algebras from hyperbolic actions
研究基于群作用的 $C^{*}$-代数的简性，定义作用基 $C^{*}$-代数并证明其简性条件，应用显示大映射类群满足简性条件。
We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a unique tracial state, but is not simple. Moreover, we show that there is a radical class of groups for which the reduced group C*-algebra of any group is simple precisely when the group has a trivial radical corresponding to this class.
Nekrashevych algebras of self-similar group actions are natural generalizations of the classical Leavitt algebras. They are discrete analogues of the corresponding Nekrashevych $C^\ast$-algebras. In particular, Nekrashevych, Clark, Exel, Pardo, Sims and Starling have studied the question of simplicity of Nekrashevych algebras, in part, because non-simplicity of the complex algebra implies non-simplicity of the $C^\ast$-algebra. In this paper we give necessary and sufficient conditions for the Nekrashevych algebra of a contracting group to be simple. Nekrashevych algebras of contracting groups …
A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras is given and applied to $C^*$-algebras of subshifts.
By exploiting properties of boundaries associated with Coxeter groups we obtain a complete characterization of simple right-angled multi-parameter Hecke C$^{\ast}$-algebras. This extends previous results by Caspers, Larsen and the author. Based on work by Raum and Skalski, we further describe the center and the character space of right-angled Hecke C$^{\ast}$-algebras.
We develop a framework suitable for obtaining simplicity criteria for reduced $C^*$-algebras of Hausdorff etale groupoids. This is based on the study of certain non-degenerate $C^*$-subalgebras (in the case of groupoids, the $C^*$-algebra of the interior isotropy bundle), for which one can control (non-unique) state extensions to the ambient C*-algebra. As an application, we give simplicity criteria for reduced crossed products of abelian $C^*$-algebras by discrete groups.
Simplicity and tracial weights on non-unital reduced crossed products
本文在温和假设下将单位约化交叉积的定理推广至非单位情形，证明了C*-代数简单性及迹权重唯一性在离散C*-单群上的稳定性，并应用于局部紧群扩张与扭曲交叉积。
In this paper, we consider the simplicity of the C*-algebra associated to an arbitrary weakly left-resolving labeled space (E, L, E), where E is the smallest non-degenerate accommodating set. We classify all gauge-invariant ideals of C*(E, L, E) and characterize minimality of (E, L, E) in terms of ideal structure of C*(E, L, E). Using these results, we prove simplicity results for C*-algebras associated to arbitrary labeled spaces.
A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.
This paper studies simplicity, primitivity and semiprimitivity of algebras associated to étale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and can be used to recover the known primitivity criterion for Leavitt path algebras.
A countable group is C*-simple if its reduced C*-algebra is simple. It is well known that C*-simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.
We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra associated to non-Hausdorff étale groupoids. Then we show how our results apply in the setting of tight representations of inverse semigroups, groups acting on graphs, and self-similar actions. In particular, we show that C*-algebra and the complex Steinberg algebra of the self-similar action of the Grigorchuk group are simple but the Steinberg algebra with coef…
It is shown that no local periodicity is equivalent to the aperiodicity condition for arbitrary finitely-aligned k-graphs. This allows us to conclude that C*(Λ) is simple if and only if Λis cofinal and has no local periodicity.
In this article we initiate research on locally compact C*-simple groups. We first show that every C*-simple group must be totally disconnected. Then we study C*-algebras and von Neumann algebras associated with certain groups acting on trees. After formulating a locally compact analogue of Powers' property, we prove that the reduced group C*-algebra of such groups is simple. This is the first simplicity result for C*-algebras of non-discrete groups and answers a question of de la Harpe. We also consider group von Neumann algebras of certain non-discrete groups acting on trees. We prove factor…
We realize Leavitt ultragraph path algebras as partial skew group rings. Using this realization we characterize artinian ultragraph path algebras and give simplicity criteria for these algebras.
We have introduced a notion of $C^*$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^*$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^*$-algebra with some conditions. The endomorphisms are indexed by symbols and yield both a subshift and a $C^*$-algebra of a Hilbert $C^*$-bimodule. The associated $C^*$-algebra with the $C^*$-symbolic dynamical system is regarded as a crossed product by the subshift. We will study a simplicity condition of the $C^*$-algebras of the $C^*$-symbolic dynamical systems. Some ex…
Suzuki recently gave constructions of non-discrete examples of locally compact C*-simple groups and Raum showed C*-simplicity of the relative profinite completions of the Baumslag-Solitar groups by using Suzuki's results. We extend this result to some fundamental groups of graphs of groups called generalized Baumslag-Solitar groups. In this article, we focus on some sufficient condition to show that these locally compact groups are C*-simple and that KMS-weights of these reduced group C*-algebras are unique. This condition is an analogue of the Powers averaging property of discrete groups and …
Graph products of groups were introduced by Green in her thesis. They have an operator algebraic counterpart introduced and explored by Fima and the first-named author. In this paper we prove Khintchine type inequalities for general C$^{\ast}$-algebraic graph products which generalize results by Ricard and Xu on free products of C$^{\ast}$-algebras. We apply these inequalities in the context of (right-angled) Hecke C$^{\ast}$-algebras, which are deformations of the group algebra of Coxeter groups. For these we deduce a Haagerup inequality. We further use this to study the simplicity and trace …
We prove simplicity and pure infiniteness results for a certain class of labelled graph $C^*$-algebras. We show, by example, that this class of unital labelled graph $C^*$-algebras is strictly larger than the class of unital graph $C^*$-algebras.
A necessary and sufficient condition for the simplicity of the C*-algebra reduced free product of finite dimensional abelian algebras is found, and it is proved that the stable rank of every such free product is 1. Related results about other reduced free products of C*-algebras are proved.
We prove simplicity of all intermediate $C^*$-algebras $C^*_{r}(Γ)\subseteq \mathcal{B} \subseteq Γ\ltimes_r C(X)$ in the case of minimal actions of $C^*$-simple groups $Γ$ on compact spaces $X$. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar (arXiv:1712.10133v2). We show that the Powers' averaging property holds for the reduced crossed product $Γ\ltimes_r \mathcal{A}$ for any action $Γ\curvearrowright \mathcal{A}$ of a $C^*$-simple group $Γ$ on a unital $C^*$-algebra $\mathcal{A}$, and use it to prove a one-to-one correspondence between stationar…
An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity
本文将Li-Yang的自相似k-图及其C*-代数推广到任意有限对齐k-图，并借助逆半群模型分析其紧群胚与C*-代数结构，为研究单纯性提供了新工具。
In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an ultragraph algebra to be purely infinite and to be AF. Using these techniques we also produce an example of an ultragraph algebra which is neither a graph algebra nor an Exel-Laca algebra. We conclude by proving that the C*-algebras of ultragraphs with no sinks are Cuntz-Pimsner algebras.
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a Cuntz-Pimsner algebra $C^*(Q).$ Given $Γ$ a locally compact group and $α$ and $β$ endomorphisms on $Γ,$ one may construct a topological quiver $Q_{α,β}(Γ)$ with vertex set $Γ,$ and edge set $Ω_{α,β}(Γ)= \{(x,y)\inΓ\timesΓ\| α(y)=β(x)\}.$ In \cite{Mc1}, the author examined the Cuntz-Pimsner algebra $\cal{O}_{α,β}(Γ):=C^*(Q_{α,β}(Γ))$ and found generators (and …
Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show that the image of this representation generates $C^*(G)$ if and only if $C^*(G)$ admits no tracial state. The techniques that we use include the notion of groups covering groupoids. As an application, we provide sufficient conditions for $C^*$-simplicity of certain topological full groups, including those associated with topologically free and minimal actions of non-amenable and countable groups on t…
We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid of the k-graph then acts on the cartesian product of the infinite-path space of the graph with the dual group of the centre of any bicharacter representing this second-cohomology class. The twisted k-graph algebra is simple if and only if this action is minimal. We apply this result to characterise simplicity for many twisted crossed products of k-graph algeb…
Simplicity and pure infiniteness for $\text{C}^*$-algebras associated with stabilizers of boundary actions
该研究针对离散群作用于紧空间的稳定子相关C*-代数，利用Rieffel诱导方法，证明当空间为极端边界时，对应群C*-代数纯无限，回答了汤普森群相关C*-代数的部分问题
In 2016, I solved a problem of de la Harpe in 2006: Is there a non-discrete C*-simple group? However the solution was not fully satisfactory as the provided C*-simple groups (and their operator algebras) are very close to discrete groups. All previously known examples are of this form. In this article I give yet another construction of non-discrete C*-simple groups. The statement in the title then follows. This in particular gives the first examples of non-elementary C*-simple groups (in Wesolek's sense).
On the simplicity of Katsura algebras
研究桂田代数及相关斯坦伯格代数的单性，借助自相似群胚模型刻画奇异理想消失情况，给出类似结果，还描述了判定奇异理想消失的算法及提供了相关非豪斯多夫例子。
We characterize when the reduced C*-algebra of a group has unique tracial state, respectively, is simple, in terms of Dixmier-type properties of the group C*-algebra. We also give a simple proof of the recent result by Breuillard, Kalantar, Kennedy and Ozawa that the reduced C*-algebra of a group has unique tracial state if and only if the amenable radical of the group is trivial.
A countable group is C*-simple if its reduced C*-algebra is a simple algebra. Since Powers recognised in 1975 that non-abelian free groups are C*-simple, large classes of groups which appear naturally in geometry have been identified, including non-elementary Gromov hyperbolic groups and lattices in semisimple groups. In this exposition, C*-simplicity for countable groups is shown to be an extreme case of non-amenability. The basic examples are described and several open problems are formulated.
In this paper, we prove that the algebra of an étale groupoid with totally disconnected unit space has a simple algebra over a field if and only if the groupoid is minimal and effective and the only function of the algebra that vanishes on every open subset is the null function. Previous work on the subject required the groupoid to be also topologically principal in the non-Hausdorff case, but we do not. Furthermore, we provide the first examples of minimal and effective but not topologically principal étale groupoids with totally disconnected unit spaces. Our examples come from self-similar g…
We consider conditions on a $k$-graph $Λ$, a semigroup $S$ and a functor $η: Λ\to S$ which ensure that the $C^*$-algebra of the skew-product graph $Λ\times_ηS$ is simple. Our results allow give some necessary and sufficient conditions for the AF-core of a $k$-graph $C^{*}$-algebra to be simple.
Simplicity of $L^p$-graph algebras
本文证明了对任意可数有向图，$L^p$-算子图代数作为 Banach 代数的（纯无限）单性与 Leavitt 路径代数作为环的（纯无限）单性等价。
Pimsner introduced the C*-algebra O_X generated by a Hilbert bimodule X over a C*-algebra A. We look for additional conditions that X should satisfy in order to study simplicity and, more generally, the ideal structure of O_X when X is finite projective. We introduce two conditions: `(I)-freeness' and `(II)-freeness', stronger than the former, in analogy with [J. Cuntz, W. Krieger, Invent. Math. 56, 251-268] and [J. Cuntz, Invent. Math. 63, 25-40] respectively. (I)-freeness comprehend the case of the bimodules associated with an inclusion of simple C*-algebras with finite index, real or pseudo…
Simplicity of twisted C*-algebras of Deaconu--Renault groupoids
本文研究有限秩自由交换幺半群局部同胚作用所生成 Deaconu–Renault 群胚的扭曲 C*-代数，证明在群胚极小的前提下其单性等价于迷向内部扭曲代数谱上的商作用极小，并给出拓扑图 C*-代数交叉积应用。
Simplicity of Cuntz-Pimsner algebras of quantum graphs
本文研究了无量子源的量子图的Cuntz-Pimsner代数单纯性，给出了充分条件并定义了到相对代数的满射，首次构造了具有不同量子Cuntz-Krieger与局部代数的量子图实例。
We prove that if Λis a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if Λis cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) is equivalent to a suitably modified version of Robertson and Steger's original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinality and aperiodicity of Λin terms of ideals in C^*(Λ).
Simplicity of reduced crossed products
该研究通过稳定子群刻画了极小G-流对应的约化交叉积C*-代数的单纯性，证明其单纯性等价于X中点的C*-单纯稳定子群条件，并给出不可数群不适用该结果的例子，解决了Ozawa的问题。
We show that the commutator subgroup of the group of unitaries connected to the identity in a simple unital C*-algebra is simple modulo its center. We then go on to investigate the role of regularity properties in the structure of the special unitary group of a C*-algebra. Under mild assumptions, we show that this group has the invariant automatic continuity property and a unique polish group topology. Strengthening our assumptions in the case of simple C*-algebras, we show that the special unitary group modulo its center has bounded normal generation. These results apply to all simple purely …
The main result here is that a simple separable C*-algebra is Z-stable (where Z denotes the Jiang-Su algebra) if (i) it has finite nuclear dimension or (ii) it is approximately subhomogeneous with slow dimension growth. This generalizes the main results of [Toms, "K-theoretic rigidity and slow dimension growth"; Winter, "Nuclear dimension and Z-stability of pure C*-algebras"] to the nonunital setting. As a consequence, finite nuclear dimension implies Z-stability even in the case of a separable C*-algebra with finitely many ideals. Algebraic simplicity is established as a fruitful weakening of…
This paper studies injective envelopes of groupoid dynamical systems and the corresponding boundaries. Analogue to the group case, we associate a bundle of compact Hausdorff spaces to any (discrete) groupoid (the Hamana boundary of the groupoid). We study bundles of compact topological spaces equipped with an action of a groupoid. We show that any groupoid has a minimal boundary (the Furstenberg boundary of the groupoid). We prove that the Hamana and Furstenberg boundaries are the same, for (discrete) groupoids. We find the relation between the reduced crossed product of the $\G$-injective env…
We study simplicity and pure infiniteness criteria for C*-algebras associated to inverse semigroup actions by Hilbert bimodules and to Fell bundles over etale not necessarily Hausdorff groupoids. Inspired by recent work of Exel and Pitts, we introduce essential crossed products for which there are such criteria. In our approach the major role is played by a generalised expectation with values in the local multiplier algebra. We give a long list of equivalent conditions characterising when the essential and reduced C*-algebras coincide. Our most general simplicity and pure infiniteness criteria…
On simplicity of Cuntz algebra and its generalizations
本文综述 Cuntz 代数及其多种推广代数的构造，并梳理保证其单纯性的条件，尤其讨论约化 Cuntz-Nica-Pimsner 代数的充分条件及其对 Elliott 分类计划的意义。
We prove that the C*-algebra of a second-countable, étale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated complex *-algebra introduced by Steinberg is simple if and only if the interior of the isotropy subgroupoid of G is equal to the unit space and G is minimal.
Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple, $E^0$ has no nontrivial hereditary and saturated subset, and every cycle in $E$ has an exit. We also give a complete description of the center of a simple Leavitt path algebra.
In previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λwith no sources is simple if and only if Λis both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing's "removing sources" construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.
A characterization of simplicity of reduced groupoid C*-algebras
本文刻画了约化群胚C*-代数的简单性，证明其等价于存在余稠密单位点集具有C*-简单迷向群，并构造反例回答Christensen和Neshveyev的问题。
Given a partial action $π$ of an inverse semigroup $S$ on a ring $\mathcal{A}$ one may construct its associated skew inverse semigroup ring $\mathcal{A} \rtimes_πS$. Our main result asserts that, when $\mathcal{A}$ is commutative, the ring $\mathcal{A} \rtimes_πS$ is simple if, and only if, $\mathcal{A}$ is a maximal commutative subring of $\mathcal{A} \rtimes_πS$ and $\mathcal{A}$ is $S$-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. Furthermore,…
Simplicity of q-Gaussian C*-algebras
证明 q ∈ (-1,1) 时 q-高斯 C*-代数具有 Dixmier 平均性质，从而单且具有唯一迹，方法结合快速衰减与自由概率得到的生成元交换子谱隙估计。
We give a combinatorial description of a family of 2-graphs which subsumes those described by Pask, Raeburn and Weaver. Each 2-graph $Λ$ we consider has an associated $C^*$-algebra, denoted $C^*(Λ)$, which is simple and purely infinite when $Λ$ is aperiodic. We give new, straightforward conditions which ensure that $Λ$ is aperiodic. These conditions are highly tractable as we only need to consider the finite set of vertices of $Λ$ in order to identify aperiodicity. In addition, the path space of each 2-graph can be realised as a two-dimensional dynamical system which we show must have zero ent…
$C^*$-simplicity, confined subalgebras, and operator algebraic uniform recurrence
本文研究了群von Neumann代数中的受限子代数，提出均匀递归态的概念，并证明可数离散群C*-简单当且仅当不存在非平凡可及受限子代数。
A discrete group $Γ$ is C*-simple if the C*-algebra $C_λ^*(Γ)$ generated by the range of the left regular representation $λ$ on $\ell^2(Γ)$ is simple. In this case, $Γ$ acts faithfully on the Furstenberg boundary $\partial_FΓ$ and there is a unique trace on $C_λ^*(Γ)$. In this paper we study the unique trace property for the C*-algebra $C_π^*(Γ)$ generated by the range of an arbitrary unitary representation $π: Γ\to B(H_π) $ and relate it to the faithfulness of the action of $Γ$ on the Furstenberg-Hamana boundary $\mathcal B_π$. Similar relation is obtained between simplicity of $C_π^*(Γ)$ and…
Let R0 be a commutative associative ring (not necessarily unital), G a group and alpha a partial action by ideals that contain local units. We show that R0 is maximal commutative in the partial skew group ring R0*G if and only if R0 has the ideal intersection property in R0*G. From this we derive a criterion for simplicity of R0*G in terms of maximal commutativity and $G-$simplicity of R0 and apply this to two examples, namely to partial actions by clopen subsets of a compact set and to give a new proof of the simplicity criterion for Leavitt path algebras. A new proof of the Cuntz-Krieger uni…
In this article, we consider a twisted partial action $α$ of a group $G$ on a ring $R$ and it is associated partial crossed product $R*_α^wG$. We study necessary and sufficient conditions for the commutativity and simplicity of $R*_α^wG$. Let $R=C(X)$ the algebra of continuous functions of a topological space $X$ on the complex numbers and $C(X)*_αG$ the partial skew group ring, where $α$ is a partial action of a topological group $G$ on $C(X)$. We study some topological properties to obtain results on the algebra $C(X)$. Also, we study the simplicity of $C(X)*_αG$ using topological properties…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。