arXiv: Operator Algebras最新文献_第3页

Connes’s trace theorem for curved noncommutative tori: Application to scalar curvature 弯曲非交换环面的cones迹定理:在标量曲率上的应用

arXiv: Operator Algebras Pub Date : 2019-12-15 DOI: 10.1063/5.0005052

Raphael Ponge

引用次数: 7

Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results 非交换环上的非交换剩余和正则迹。唯一性结果

arXiv: Operator Algebras Pub Date : 2019-11-27 DOI: 10.3842/sigma.2020.061

Raphael Ponge

引用次数: 7

A Fejér theorem for boundary quotients arising from algebraic dynamical systems 代数动力系统边界商的fejsamir定理

arXiv: Operator Algebras Pub Date : 2019-11-08 DOI: 10.2422/2036-2145.201903_007

Valeriano Aiello, R. Conti, S. Rossi

引用次数: 4

Braided Free Orthogonal Quantum Groups 编织自由正交量子群

arXiv: Operator Algebras Pub Date : 2019-10-29 DOI: 10.1093/imrn/rnaa379

R. Meyer, Sutanu Roy

引用次数: 5

𝐶*-algebras, groupoids and covers of shift spaces 位移空间的<s:1> -代数、群拟和覆盖

arXiv: Operator Algebras Pub Date : 2019-10-04 DOI: 10.1090/btran/53

K. Brix, T. M. Carlsen

{"title":"𝐶*-algebras, groupoids and covers of shift spaces","authors":"K. Brix, T. M. Carlsen","doi":"10.1090/btran/53","DOIUrl":"https://doi.org/10.1090/btran/53","url":null,"abstract":"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 associated two-sided shift spaces $Lambda_{mathsf{X}}$ and $Lambda_{mathsf{Y}}$ in terms of isomorphism of the stabilized groupoids $mathcal{G}_{mathsf{X}}times mathcal{R}$ and $mathcal{G}_{mathsf{Y}}times mathcal{R}$, and diagonal preserving $^*$-isomorphism of the stabilized $mathrm{C^*}$-algebras $mathcal{O}_{mathsf{X}}otimes mathbb{K}$ and $mathcal{O}_{mathsf{Y}}otimes mathbb{K}$. Our strategy is to lift relations on the shift spaces to similar relations on the covers. Restricting to the class of sofic shifts whose groupoids are essentially principal, we find that the pair $(mathcal{O}_{mathsf{X}}, C(mathsf{X}))$ remembers the continuous orbit equivalence class of $mathsf{X}$ while the pair $(mathcal{O}_{mathsf{X}}otimes mathbb{K}, C(mathsf{X})otimes c_0)$ remembers the flow equivalence class of $Lambda_{mathsf{X}}$. In particular, continuous orbit equivalence implies flow equivalence for this class of shift spaces.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"95 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133847090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Maximal Rigid Subalgebras of Deformations and $L^2$ Cohomology, II 变形的极大刚性子代数与L^2上同调，2

arXiv: Operator Algebras Pub Date : 2019-09-09 DOI: 10.14288/1.0389705

Rolando de Santiago, Ben Hayes, D. Hoff, Thomas Sinclair

{"title":"Maximal Rigid Subalgebras of Deformations and $L^2$ Cohomology, II","authors":"Rolando de Santiago, Ben Hayes, D. Hoff, Thomas Sinclair","doi":"10.14288/1.0389705","DOIUrl":"https://doi.org/10.14288/1.0389705","url":null,"abstract":"In the past two decades, Sorin Popa's breakthrough deformation/rigidity theory has produced remarkable rigidity results for von Neumann algebras $M$ which can be deformed inside a larger algebra $widetilde M supseteq M$ by an action $alpha: mathbb{R} to {rm Aut}(widetilde M)$, while simultaneously containing subalgebras $Q$ {it rigid} with respect to that deformation, that is, such that $alpha_t to {rm id}$ uniformly on the unit ball of $Q$ as $t to 0$. However, it has remained unclear how to exploit the interplay between distinct rigid subalgebras not in specified relative position. \u0000We show that in fact, any diffuse subalgebra which is rigid with respect to a mixing s-malleable deformation is contained in a subalgebra which is uniquely maximal with respect to being rigid. In particular, the algebra generated by any family of rigid subalgebras that intersect diffusely must itself be rigid with respect to that deformation. The case where this family has two members was the motivation for this work, showing for example that if $G$ is a countable group with $beta^{1}_{(2)}(G) > 0$, then $L(G)$ cannot be generated by two property $(T)$ subalgebras with diffuse intersection; however, the result is most striking when the family is infinite.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"1009 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123098056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Relative entropy for von Neumann subalgebras 冯诺依曼子代数的相对熵

arXiv: Operator Algebras Pub Date : 2019-09-04 DOI: 10.1142/s0129167x20500469

Li Gao, M. Junge, Nicholas Laracuente

引用次数: 22

A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries 具有现场有限群对称的满足分裂性质的量子自旋链上的纯态分类

arXiv: Operator Algebras Pub Date : 2019-08-22 DOI: 10.1090/BTRAN/51

Y. Ogata

引用次数: 21

Angles between Haagerup–Schultz projections and spectrality of operators 哈格鲁-舒尔茨投影与算子频谱之间的夹角

arXiv: Operator Algebras Pub Date : 2019-07-24 DOI: 10.1016/j.jfa.2021.109027

K. Dykema, Amudhan Krishnaswamy-Usha