群胚有限对齐子范畴上乘积系统的余泛$C^{\ast}$-代数

与不同Haar系统相关的同构广群$C^{\ast}$ -代数

Isomorphic groupoid $C^{\ast}$-algebras associated with different Haar systems

我们将考虑一个局部紧广群，它被赋予一个Haar系统并具有真轨道空间。我们将构造一个独立于Haar系的群胚C* 代数-代数（直到一个 *-同构）.

余圈扭变变换群胚的 $C^{\ast}$-代数的度量维数：增长与动力复杂性

Metric dimension of $C^{\ast}$-algebras of cocycle twisted transformation groupoids: Growth and dynamical complexity

研究通过分层cLip-范数在扭变变换群胚C*-代数上构造CQMS结构，证明了当群为多项式增长时度量维数有上界，指数增长时维数无穷，揭示了群增长二分法在余圈扭变下的保持性。

关于平展广群代数中的投影与保对角同态的注记

A note on projections in étale groupoid algebras and diagonal preserving homomorphisms

本文刻画了满足“豪斯多夫充足广群代数的任意$\ast$-同态均自动保对角”性质的环，其恰好是Carlsen研究的复数共轭闭子环，且给出了比Leavitt路代数情形更简洁的广群层面证明。

来自群胚同调理论同构的K-理论同构

Isomorphisms in K-theory from isomorphisms in groupoid homology theories

该研究证明无挠顺从充裕群胚中由平展对应诱导的群胚同调同构可导出相关$\text{C}^\text{*}$-代数K-理论同构，借此推广了X. Li的左正则逆半群$\text{C}^\text{*}$-代数K-理论公式，核心方法是发展ABC谱序列的函子性。

Topological Lattice Defects by Groupoid Methods and Kasparov's KK-Theory

The bulk-boundary and a new bulk-defect correspondence principles are formulated using groupoid algebras. The new strategy relies on the observation that the groupoids of lattices with boundaries or defects display spaces of units with invariant accumulation manifolds, hence they can be naturally split into disjoint unions of open and closed invariant sub-sets. This leads to standard exact sequences of groupoid $C^\ast$-algebras that can be used to associate a Kasparov element to a lattice defect and to formulate an extremely general bulk-defect correspondence principle. As an application, we …

超图$C^{*}$ -代数的群胚和逆半群表示

Groupoid and Inverse Semigroup Presentations of Ultragraph $C^{*}$-Algebras

受Paterson关于有向图的$C^{\ast}$ -代数的工作的启发，我们展示了如何将广群$\mathfrak{G}_{\mathcal{G}}$与超图$\mathcal{G}$相关联，使得$\mathfrak{G}_{\mathcal{G}}$的$C^*$ -代数与Tomforde的$C^*$ -代数$C^*(\mathcal{G})$正则同构.群胚$\mathfrak{G}_{\mathcal{G}}$是从自然关联到$\mathcal{G}$的逆半群$S_{\mathcal{G}}$构建的。

Cocycles on Certain Groupoids Associated to $ \mathbb{N}^{k} $-Actions

We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new characterization of $ 1 $-cocycles on these groupoids taking values in a locally compact abelian group, given in terms of $ k $-tuples of continuous functions on the unit space satisfying certain canonical identities. Using this, we develop an extended Ruelle-Perron-Frobenius theory for dynamical systems of several commuting operators ($ k $-Ruelle triples and c…

A groupoid approach to interacting fermions

We consider the algebra $\dotΣ(\mathcal L)$ generated by the inner-limit derivations over the ${\rm GICAR}$ algebra of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to the aperiodic lattice, we demonstrate that the image of $\dot Σ(\mathcal L)$ through the Fock representation can be completed to a groupoid-solvable pro-$C^\ast$-algebra. Our result is the first step towards unlocking the $K$-theoretic tools available for separable $C^\ast$-algebra for applicatio…

同步动力系统：其群胚与 $C^*$-代数

Synchronizing Dynamical Systems: their groupoids and $C^*$-algebras

本文提出同步动力系统以推广 Smale 空间，并研究其相关 $C^\ast$-代数，证明其同宿代数含具有类似 Smale 空间同宿代数行为的理想。

群与群胚自相似作用的同调与K-理论

Homology and K-theory for self-similar actions of groups and groupoids

本文为自相似群作用构造长正合序列，计算其群胚同调和C*-代数K-理论，并证明包含Grigorchuk群的Röver单群有理无环但Schur乘子非平凡。

阿贝尔基塔耶夫模型的全部KMS态集

The Full Set of KMS-States for Abelian Kitaev Models

本文研究了阿贝尔基塔耶夫模型的KMS态，通过证明生成子代数与UHF代数的包含关系，构建了群oid C*代数，并证明了在β≥0时KMS态的唯一性及β→∞时极限态与无 frustrations 地面态一致。

关于 $\mathrm{C}^\ast$-代数的 Pedersen 理想上的自伴迹

Self-adjoint traces on the Pedersen ideal of $\mathrm{C}^\ast$-algebras

本文系统研究 $\mathrm{C}^\ast$-代数 Pedersen 理想上的自伴迹集合 $T_{\mathbb R}(A)$，建立其 Kadison 对偶，计算主扭平展群胚代数的该集合，并对一大类代数正面回答迹问题。

收缩自相似群的$C^*$-代数的单性

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。

基于 $AF$-代数的二维替换铺嵌空间的 $K$-理论

$K$-theory of two-dimensional substitution tiling spaces from $AF$-algebras

本文证明在合理假设下，二维替换铺嵌空间不稳定广群 $C^\ast$-代数的 $K$-理论可由替换规则及其 $1$-骨架类似物的 $AF$-代数 $K$-理论显式重构，通过相对 $K$-理论与切除转化为纯拓扑正合序列，并给出 Sage 计算示例。

K-theory of the Chair Tiling via AF-algebras

We compute the $K$-theory groups of the groupoid C$^\ast$-algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the $K$-theory groups of the $AF$-algebras of the substitution and the induced lower dimensional substitutions on edges and vertices.