arXiv - MATH - Operator Algebras最新文献_第3页

Bockstein operations and extensions with trivial boundary maps 具有琐碎边界映射的博克斯坦运算和扩展

arXiv - MATH - Operator Algebras Pub Date : 2024-08-30 DOI: arxiv-2408.17055

Qingnan An, Zhichao Liu

引用次数: 0

Classification of homomorphisms from $C(Ω)$ to a $C^*$-algebra 从 $C(Ω)$ 到 $C^*$ 代数的同态分类

arXiv - MATH - Operator Algebras Pub Date : 2024-08-29 DOI: arxiv-2408.16657

Qingnan An, George Elliott, Zhichao Liu

引用次数: 0

Sofic actions on graphs 图上的索非克作用

arXiv - MATH - Operator Algebras Pub Date : 2024-08-28 DOI: arxiv-2408.15470

David Gao, Greg Patchell, Srivatsav Kunnawalkam Elayavalli

{"title":"Sofic actions on graphs","authors":"David Gao, Greg Patchell, Srivatsav Kunnawalkam Elayavalli","doi":"arxiv-2408.15470","DOIUrl":"https://doi.org/arxiv-2408.15470","url":null,"abstract":"We develop a theory of soficity for actions on graphs and obtain new\u0000applications to the study of sofic groups. We establish various examples,\u0000stability and permanence properties of sofic actions on graphs, in particular\u0000soficity is preserved by taking several natural graph join operations. We prove\u0000that an action of a group on its Cayley graph is sofic if and only if the group\u0000is sofic. We show that arbitrary actions of amenable groups on graphs are\u0000sofic. Using a graph theoretic result of E. Hrushovski, we also show that\u0000arbitrary actions of free groups on graphs are sofic. Notably we show that\u0000arbitrary actions of sofic groups on graphs, with amenable stabilizers, are\u0000sofic, settling completely an open problem from cite{gao2024soficity}. We also\u0000show that soficity is preserved by taking limits under a natural\u0000Gromov-Hausdorff topology, generalizing prior work of the first author\u0000cite{gao2024actionslerfgroupssets}. Our work sheds light on a family of groups\u0000called graph wreath products, simultaneously generalizing graph products and\u0000generalized wreath products. Extending various prior results in this direction\u0000including soficity of generalized wreath products cite{gao2024soficity}, B.\u0000Hayes and A. Sale cite{HayesSale}, and soficity of graph products cite{CHR,\u0000charlesworth2021matrix}, we show that graph wreath products are sofic if the\u0000action and acting groups are sofic. These results provide several new examples\u0000of sofic groups in a systematic manner.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195040","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: 0

A latticed total K-theory 有格全 K 理论

arXiv - MATH - Operator Algebras Pub Date : 2024-08-28 DOI: arxiv-2408.15941

Qingnan An, Chunguang Li, Zhichao Liu

引用次数: 0

The ideal separation property for reduced group $C^*$-algebras 还原组 $C^*$ 算法的理想分离特性

arXiv - MATH - Operator Algebras Pub Date : 2024-08-27 DOI: arxiv-2408.14880

Are Austad, Hannes Thiel

引用次数: 0

Universal covering groups of unitary groups of von Neumann algebras 冯-诺依曼代数单元群的普遍覆盖群

arXiv - MATH - Operator Algebras Pub Date : 2024-08-25 DOI: arxiv-2408.13710

Pawel Sarkowicz

引用次数: 0

A Khintchine inequality for central Fourier series on non-Kac compact quantum groups 非 Kac 紧凑量子群上中心傅里叶级数的 Khintchine 不等式

arXiv - MATH - Operator Algebras Pub Date : 2024-08-24 DOI: arxiv-2408.13519

Sang-Gyun Youn

引用次数: 0

The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $log$-algebras 交换代数的同构与非交换代数的同构之间的相互关系

arXiv - MATH - Operator Algebras Pub Date : 2024-08-24 DOI: arxiv-2408.13527

Rustam Abdullaev, Azizkhon Azizov

引用次数: 0

Conditional representation stability, classification of $*$-homomorphisms, and eta invariants 条件表示稳定性、$*$同构的分类和 eta 不变量

arXiv - MATH - Operator Algebras Pub Date : 2024-08-23 DOI: arxiv-2408.13350

Rufus Willett

{"title":"Conditional representation stability, classification of $*$-homomorphisms, and eta invariants","authors":"Rufus Willett","doi":"arxiv-2408.13350","DOIUrl":"https://doi.org/arxiv-2408.13350","url":null,"abstract":"A quasi-representation of a group is a map from the group into a matrix\u0000algebra (or similar object) that approximately satisfies the relations needed\u0000to be a representation. Work of many people starting with Kazhdan and\u0000Voiculescu, and recently advanced by Dadarlat, Eilers-Shulman-So{}rensen and\u0000others, has shown that there are topological obstructions to approximating\u0000unitary quasi-representations of groups by honest representations, where\u0000`approximation' is understood to be with respect to the operator norm. The purpose of this paper is to explore whether approximation is possible if\u0000the known obstructions vanish, partially generalizing work of Gong-Lin and\u0000Eilers-Loring-Pedersen for the free abelian group of rank two, and the Klein\u0000bottle group. We show that this is possible, at least in a weak sense, for some\u0000`low-dimensional' groups including fundamental groups of closed surfaces,\u0000certain Baumslag-Solitar groups, free-by-cyclic groups, and many fundamental\u0000groups of three manifolds. The techniques used in the paper are $K$-theoretic: they have their origin in\u0000Baum-Connes-Kasparov type assembly maps, and in the Elliott program to classify\u0000$C^*$-algebras; Kasparov's bivariant KK-theory is a crucial tool. The key new\u0000technical ingredients are: a stable uniqueness theorem in the sense of\u0000Dadarlat-Eilers and Lin that works for non-exact $C^*$-algebras; and an\u0000analysis of maps on $K$-theory with finite coefficients in terms of the\u0000relative eta invariants of Atiyah-Patodi-Singer. Despite the proofs going\u0000through $K$-theoretic machinery, the main theorems can be stated in elementary\u0000terms that do not need any $K$-theory.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195048","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: 0

Minimal covers with continuity-preserving transfer operators for topological dynamical systems 拓扑动力系统的最小盖与连续性保持转移算子

arXiv - MATH - Operator Algebras Pub Date : 2024-08-21 DOI: arxiv-2408.11917

Kevin Aguyar Brix, Jeremy B. Hume, Xin Li

引用次数: 0