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Journal of Noncommutative Geometry最新文献

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The 3-cyclic quantum Weyl algebras, their prime spectra and a classification of simple modules ($q$ is not a root of unity) 三环量子韦尔后代数、其素谱和简单模块的分类（$q$ 不是统一根）
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2024-01-05 DOI: 10.4171/jncg/547
V. Bavula
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引用次数: 0
Finite approximation properties of $C^{*}$-modules II C^{*}$ 模块的有限逼近特性 II
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-12-01 DOI: 10.4171/jncg/548
M. Amini
{"title":"Finite approximation properties of $C^{*}$-modules II","authors":"M. Amini","doi":"10.4171/jncg/548","DOIUrl":"https://doi.org/10.4171/jncg/548","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"14 11","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138627294","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
Nowhere scattered $C^*$-algebras 无处分散的$C^*$-代数
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-14 DOI: 10.4171/jncg/526
Hannes Thiel, Eduard Vilalta
{"title":"Nowhere scattered $C^*$-algebras","authors":"Hannes Thiel, Eduard Vilalta","doi":"10.4171/jncg/526","DOIUrl":"https://doi.org/10.4171/jncg/526","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"5 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954395","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: 0
A short proof of an index theorem, II 指数定理的一个简短证明，2
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-14 DOI: 10.4171/jncg/524
Yavar Abdolmaleki, Dan Kucerovsky
{"title":"A short proof of an index theorem, II","authors":"Yavar Abdolmaleki, Dan Kucerovsky","doi":"10.4171/jncg/524","DOIUrl":"https://doi.org/10.4171/jncg/524","url":null,"abstract":"We introduce a slight modification of the usual equivariant $KK$-theory. We use this to give a $KK$-theoretical proof of an equivariant index theorem for Dirac-Schrodinger operators on a non-compact manifold of nowhere positive curvature. We incidentally show that the boundary of Dirac is Dirac; generalizing earlier work of Baum and coworkers, and a result of Higson and Roe.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"9 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954579","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: 0
Algebraic aspects of connections: From torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials 连接的代数方面:从扭转、曲率、后李代数到加夫里洛夫的二重指数和特殊多项式
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-12 DOI: 10.4171/jncg/539
M. J. H. Al-Kaabi, K. Ebrahimi-Fard, D. Manchon, H. Z. Munthe-Kaas
{"title":"Algebraic aspects of connections: From torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials","authors":"M. J. H. Al-Kaabi, K. Ebrahimi-Fard, D. Manchon, H. Z. Munthe-Kaas","doi":"10.4171/jncg/539","DOIUrl":"https://doi.org/10.4171/jncg/539","url":null,"abstract":"Understanding the algebraic structure underlying a manifold with a general affine connection is a natural problem. In this context, A. V. Gavrilov introduced the notion of framed Lie algebra, consisting of a Lie bracket (the usual Jacobi bracket of vector fields) and a magmatic product without any compatibility relations between them. In this work we will show that an affine connection with curvature and torsion always gives rise to a post-Lie algebra as well as a $D$-algebra. The notions of torsion and curvature together with Gavrilov's special polynomials and double exponential are revisited in this post-Lie algebraic framework. We unfold the relations between the post-Lie Magnus expansion, the Grossman-Larson product and the $K$-map, $alpha$-map and $beta$-map, three particular functions introduced by Gavrilov with the aim of understanding the geometric and algebraic properties of the double-exponential, which can be understood as a geometric variant of the Baker-Campbell-Hausdorff formula. We propose a partial answer to a conjecture by Gavrilov, by showing that a particular class of geometrically special polynomials is generated by torsion and curvature. This approach unlocks many possibilities for further research such as numerical integrators and rough paths on Riemannian manifolds.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"105 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352847","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
Twisted Hodge Diamonds give rise to non-Fourier–Mukai functors 扭曲的Hodge菱形产生非fourier - mukai函子
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-08 DOI: 10.4171/jncg/543
Felix Küng
{"title":"Twisted Hodge Diamonds give rise to non-Fourier–Mukai functors","authors":"Felix Küng","doi":"10.4171/jncg/543","DOIUrl":"https://doi.org/10.4171/jncg/543","url":null,"abstract":"We apply computations of twisted Hodge diamonds to construct an infinite number of non-Fourier-Mukai functors with well behaved target and source spaces. To accomplish this we first study the characteristic morphism in order to control it for tilting bundles. Then we continue by applying twisted Hodge diamonds of hypersurfaces embedded in projective space to compute the Hochschild dimension of these spaces. This allows us to compute the kernel of the embedding into the projective space in Hochschild cohomology. Finally we use the above computations to apply the construction by A. Rizzardo, M. Van den Bergh and A. Neeman of non-Fourier-Mukai functors and verify that the constructed functors indeed cannot be Fourier-Mukai for odd dimensional quadrics. Using this approach we prove that there are a large number of Hochschild cohomology classes that can be used for this type construction. Furthermore, our results allow the application of computer-based calculations to construct candidate functors for arbitrary degree hypersurfaces in arbitrary high dimensions. Verifying that these are not Fourier-Mukai still requires the existence of a tilting bundle. In particular we prove that there is at least one non-Fourier-Mukai functor for every odd dimensional smooth quadric.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" 47","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341404","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
Poisson–Lie group structures on semidirect products 半直接产物上的泊松-李群结构
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-07 DOI: 10.4171/jncg/538
Floris Elzinga, Makoto Yamashita
{"title":"Poisson–Lie group structures on semidirect products","authors":"Floris Elzinga, Makoto Yamashita","doi":"10.4171/jncg/538","DOIUrl":"https://doi.org/10.4171/jncg/538","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"33 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432270","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: 0
Representation of commutators on Schatten $p$-classes Schatten $p$-类上换向子的表示
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-07 DOI: 10.4171/jncg/542
Lixin Cheng, Zhizheng Yu
{"title":"Representation of commutators on Schatten $p$-classes","authors":"Lixin Cheng, Zhizheng Yu","doi":"10.4171/jncg/542","DOIUrl":"https://doi.org/10.4171/jncg/542","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"34 23‐24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432528","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: 0
On isometries of spectral triples associated to $mathrm{AF}$-algebras and crossed products 与$ mathm {AF}$-代数和交叉积相关的谱三元组的等距
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-11-03 DOI: 10.4171/jncg/535
Jacopo Bassi, Roberto Conti
{"title":"On isometries of spectral triples associated to $mathrm{AF}$-algebras and crossed products","authors":"Jacopo Bassi, Roberto Conti","doi":"10.4171/jncg/535","DOIUrl":"https://doi.org/10.4171/jncg/535","url":null,"abstract":"We examine the structure of two possible candidates of isometry groups for the spectral triples on $AF$-algebras introduced by Christensen and Ivan. In particular, we completely determine the isometry group introduced by Park, and observe that these groups coincide in the case of the Cantor set. We also show that the construction of spectral triples on crossed products given by Hawkins, Skalski, White and Zacharias, is suitable for the purpose of lifting isometries.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"111 4‐6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818392","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
Simplicity of twisted C*-algebras of Deaconu–Renault groupoids Deaconu-Renault群拟的扭曲C*-代数的简单性
2区 数学
Journal of Noncommutative Geometry Pub Date : 2023-10-30 DOI: 10.4171/jncg/527
Becky Armstrong, Nathan Brownlowe, Aidan Sims
{"title":"Simplicity of twisted C*-algebras of Deaconu–Renault groupoids","authors":"Becky Armstrong, Nathan Brownlowe, Aidan Sims","doi":"10.4171/jncg/527","DOIUrl":"https://doi.org/10.4171/jncg/527","url":null,"abstract":"We consider Deaconu--Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*-algebra of such a groupoid determined by a continuous circle-valued groupoid 2-cocycle. When the groupoid is not minimal, this C*-algebra is never simple, so we focus on minimal groupoids. We describe an action of the quotient of the groupoid by the interior of its isotropy on the spectrum of the twisted C*-algebra of the interior of the isotropy. We prove that the twisted groupoid C*-algebra is simple if and only if this action is minimal. We describe applications to crossed products of topological-graph C*-algebras by quasi-free actions.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"4 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136017908","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
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