发布求助
文献互助 智能选刊 最新文献

Journal of Noncommutative Geometry最新文献

筛选
英文 中文
A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature 关于正标量曲率的一个定量相对指数定理和Gromov猜想
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-03-26 DOI: 10.4171/jncg/504
Zhizhang Xie
{"title":"A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature","authors":"Zhizhang Xie","doi":"10.4171/jncg/504","DOIUrl":"https://doi.org/10.4171/jncg/504","url":null,"abstract":"In this paper, we prove a quantitative relative index theorem. It provides a conceptual framework for studying some conjectures and open questions of Gromov on positive scalar curvature. More precisely, we prove a $lambda$-Lipschitz rigidity theorem for (possibly incomplete) Riemannian metrics on spheres with certain types of subsets removed. This $lambda$-Lipschitz rigidity theorem is asymptotically optimal. As a consequence, we obtain an asymptotically optimal $lambda$-Lipschitz rigidity theorem for positive scalar curvature metrics on hemispheres. These give positive answers to the corresponding open questions raised by Gromov. As another application, we prove Gromov's $square^{n-m}$ inequality on the bound of distances between opposite faces of spin manifolds with cube-like boundaries with a suboptimal constant. As immediate consequences, this implies Gromov's cube inequality on the bound of widths of Riemannian cubes and Gromov's conjecture on the bound of widths of Riemannian bands with suboptimal constants. Further geometric applications will be discussed in a forthcoming paper.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42087619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Anick type automorphisms and new irreducible representations of Leavitt path algebras Leavitt路径代数的Anick型自同构和新的不可约表示
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-03-01 DOI: 10.4171/jncg/489
S. Kuroda, T. G. Nam
{"title":"Anick type automorphisms and new irreducible representations of Leavitt path algebras","authors":"S. Kuroda, T. G. Nam","doi":"10.4171/jncg/489","DOIUrl":"https://doi.org/10.4171/jncg/489","url":null,"abstract":"In this article, we give a new class of automorphisms of Leavitt path algebras of arbitrary graphs. Consequently, we obtain Anick type automorphisms of these Leavitt path algebras and new irreducible representations of Leavitt algebras of type $(1, n)$.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41805085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Calabi–Yau structures for multiplicative preprojective algebras 乘法预射影代数的Calabi-Yau结构
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-02-24 DOI: 10.4171/JNCG/488
T. Bozec, D. Calaque, Sarah Scherotzke
{"title":"Calabi–Yau structures for multiplicative preprojective algebras","authors":"T. Bozec, D. Calaque, Sarah Scherotzke","doi":"10.4171/JNCG/488","DOIUrl":"https://doi.org/10.4171/JNCG/488","url":null,"abstract":"In this paper we deal with Calabi-Yau structures associated with (differential graded versions of) deformed multiplicative preprojective algebras, of which we provide concrete algebraic descriptions. Along the way, we prove a general result that states the existence and uniqueness of negative cyclic lifts for non-degenerate relative Hochschild classes.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41658277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Wheel graph homology classes via Lie graph homology 轮图同构类通过李图同构
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-02-18 DOI: 10.4171/jncg/508
Benjamin C. Ward
{"title":"Wheel graph homology classes via Lie graph homology","authors":"Benjamin C. Ward","doi":"10.4171/jncg/508","DOIUrl":"https://doi.org/10.4171/jncg/508","url":null,"abstract":"We give a new proof of the non-triviality of wheel graph homology classes using higher operations on Lie graph homology and a derived version of Koszul duality for modular operads.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49089889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Tracing projective modules over noncommutative orbifolds 在非交换轨道上跟踪射影模
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-02-15 DOI: 10.4171/jncg/487
Sayan Chakraborty
{"title":"Tracing projective modules over noncommutative orbifolds","authors":"Sayan Chakraborty","doi":"10.4171/jncg/487","DOIUrl":"https://doi.org/10.4171/jncg/487","url":null,"abstract":"For an action of a finite cyclic group $F$ on an $n$-dimensional noncommutative torus $A_theta,$ we give sufficient conditions when the fundamental projective modules over $A_theta$, which determine the range of the canonical trace on $A_theta,$ extend to projective modules over the crossed product C*-algebra $A_theta rtimes F.$ Our results allow us to understand the range of the canonical trace on $A_theta rtimes F$, and determine it completely for several examples including the crossed products of 2-dimensional noncommutative tori with finite cyclic groups and the flip action of $mathbb{Z}_2$ on any $n$-dimensional noncommutative torus. As an application, for the flip action of $mathbb{Z}_2$ on a simple $n$-dimensional torus $A_theta$, we determine the Morita equivalence class of $A_theta rtimes mathbb{Z}_2,$ in terms of the Morita equivalence class of $A_theta.$","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47803754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
K-theory and homotopies of twists on ample groupoids K-理论与充分群胚上的扭的同拓扑
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-02-08 DOI: 10.4171/JNCG/399
Christian Bönicke
{"title":"K-theory and homotopies of twists on ample groupoids","authors":"Christian Bönicke","doi":"10.4171/JNCG/399","DOIUrl":"https://doi.org/10.4171/JNCG/399","url":null,"abstract":"This paper investigates the K-theory of twisted groupoid C*-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum–Connes conjecture with coefficients gives rise to an isomorphism between the K-theory groups of the respective twisted groupoid C*-algebras. The results are also interpreted in an inverse semigroup setting and applied to generalized Renault–Deaconu groupoids and P-graph algebras.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42495650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Noncommutative Hodge conjecture 非交换霍奇猜想
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-02-06 DOI: 10.4171/jncg/517
Xun Lin
{"title":"Noncommutative Hodge conjecture","authors":"Xun Lin","doi":"10.4171/jncg/517","DOIUrl":"https://doi.org/10.4171/jncg/517","url":null,"abstract":"The paper provides a version of the rational Hodge conjecture for $3dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in cite{perry2020integral} for admissible subcategories. We obtain examples of evidence of the Hodge conjecture by techniques of noncommutative geometry. Finally, we show that the noncommutative Hodge conjecture for smooth proper connective $3dg$ algebras is true.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41466174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Non-embeddable II$_1$ factors resembling the hyperfinite II$_1$ factor 不可嵌入的II$_1$因子类似于超有限II$_1$因子
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-01-25 DOI: 10.4171/jncg/474
Isaac Goldbring
{"title":"Non-embeddable II$_1$ factors resembling the hyperfinite II$_1$ factor","authors":"Isaac Goldbring","doi":"10.4171/jncg/474","DOIUrl":"https://doi.org/10.4171/jncg/474","url":null,"abstract":"We consider various statements that characterize the hyperfinite II$_1$ factors amongst embeddable II$_1$ factors in the non-embeddable situation. In particular, we show that\"generically\"a II$_1$ factor has the Jung property (which states that every embedding of itself into its ultrapower is unitarily conjugate to the diagonal embedding) if and only if it is self-tracially stable (which says that every such embedding has an approximate lifting). We prove that the enforceable factor, should it exist, has these equivalent properties. Our techniques are model-theoretic in nature. We also show how these techniques can be used to give new proofs that the hyperfinite II$_1$ factor has the aforementioned properties.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48147732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Noncommutative CW-spectra as enriched presheaves on matrix algebras 矩阵代数上的非交换CW谱作为富集预集
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2021-01-24 DOI: 10.4171/jncg/481
G. Arone, Ilan Barnea, T. Schlank
{"title":"Noncommutative CW-spectra as enriched presheaves on matrix algebras","authors":"G. Arone, Ilan Barnea, T. Schlank","doi":"10.4171/jncg/481","DOIUrl":"https://doi.org/10.4171/jncg/481","url":null,"abstract":"Motivated by the philosophy that C∗-algebras reflect noncommutative topology, we investigate the stable homotopy theory of the (opposite) category of C∗-algebras. We focus on C∗-algebras which are non-commutative CW-complexes in the sense of [ELP]. We construct the stable ∞-category of noncommutative CW-spectra, which we denote by NSp. Let M be the full spectral subcategory of NSp spanned by “noncommutative suspension spectra” of matrix algebras. Our main result is that NSp is equivalent to the ∞-category of spectral presheaves on M. To prove this we first prove a general result which states that any compactly generated stable ∞-category is naturally equivalent to the ∞category of spectral presheaves on a full spectral subcategory spanned by a set of compact generators. This is an ∞-categorical version of a result by Schwede and Shipley [ScSh1]. In proving this we use the language of enriched ∞-categories as developed by Hinich [Hin2, Hin3]. We end by presenting a “strict” model for M. That is, we define a category Ms strictly enriched in a certain monoidal model category of spectra Sp. We give a direct proof that the category of Sp-enriched presheaves Mop s → Sp M with the projective model structure models NSp and conclude that Ms is a strict model for M.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45178280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks 李群拟和可微堆上主束上的Atiyah序列与连接
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2020-12-15 DOI: 10.4171/jncg/486
I. Biswas, Saikat Chatterjee, Praphulla Koushik, F. Neumann
{"title":"Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks","authors":"I. Biswas, Saikat Chatterjee, Praphulla Koushik, F. Neumann","doi":"10.4171/jncg/486","DOIUrl":"https://doi.org/10.4171/jncg/486","url":null,"abstract":"We construct and study general connections on Lie groupoids and differentiable stacks as well as on principal bundles over them using Atiyah sequences associated to transversal tangential distributions.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44970331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信