{"title":"HPD-invariance of the Tate conjecture(s)","authors":"Gonçalo Tabuada","doi":"10.4171/jncg/462","DOIUrl":"https://doi.org/10.4171/jncg/462","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42008690","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}
{"title":"Homotopy Rota–Baxter operators and post-Lie algebras","authors":"Rong Tang, C. Bai, Li Guo, Y. Sheng","doi":"10.4171/jncg/466","DOIUrl":"https://doi.org/10.4171/jncg/466","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"2 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87208405","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}
{"title":"On the Hochschild homology of proper Lie groupoids","authors":"M. Pflaum, H. Posthuma, Xiang Tang","doi":"10.4171/jncg/467","DOIUrl":"https://doi.org/10.4171/jncg/467","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49489446","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}
{"title":"Purely infinite corona algebras and extensions","authors":"P. W. Ng","doi":"10.4171/jncg/483","DOIUrl":"https://doi.org/10.4171/jncg/483","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46281832","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}
. We prove a noncommutative generalisation of Mahler’s theorem on interpolation series, a celebrated result of p -adic analysis. Mahler’s original result states that a function from N to Z is uniformly continuous for the p -adic metric d p if and only if it can be uniformly approximated by polynomial functions. We prove an analogous result for functions from a free monoid A ∗ to a free group F ( B ) , where d p is replaced by the pro- p metric.
{"title":"A noncommutative extension of Mahler’s interpolation theorem","authors":"J. Pin, C. Reutenauer","doi":"10.4171/jncg/480","DOIUrl":"https://doi.org/10.4171/jncg/480","url":null,"abstract":". We prove a noncommutative generalisation of Mahler’s theorem on interpolation series, a celebrated result of p -adic analysis. Mahler’s original result states that a function from N to Z is uniformly continuous for the p -adic metric d p if and only if it can be uniformly approximated by polynomial functions. We prove an analogous result for functions from a free monoid A ∗ to a free group F ( B ) , where d p is replaced by the pro- p metric.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49652941","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}
{"title":"Spectral triples with multitwisted real structure","authors":"L. Dąbrowski, A. Sitarz","doi":"10.4171/jncg/450","DOIUrl":"https://doi.org/10.4171/jncg/450","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41383350","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}
{"title":"Cyclic cocycles in the spectral action","authors":"Teun D. H. van Nuland, Walter D. van Suijlekom","doi":"10.4171/jncg/500","DOIUrl":"https://doi.org/10.4171/jncg/500","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47990783","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}
Let $Asubseteq B$ be a $C^*$-inclusion. We give efficient conditions under which $A$ separates ideals in $B$, and $B$ is purely infinite if every positive element in $A$ is properly infinite in $B$. We specialise to the case when $B$ is a crossed product for an inverse semigroup action by Hilbert bimodules or a section $C^*$-algebra of a Fell bundle over an 'etale, possibly non-Hausdorff, groupoid. Then our theory works provided $B$ is the recently introduced essential crossed product and the action is essentially exact and residually aperiodic or residually topologically free. These last notions are developed in the article.
{"title":"Ideal structure and pure infiniteness of inverse semigroup crossed products","authors":"B. Kwa'sniewski, R. Meyer","doi":"10.4171/jncg/506","DOIUrl":"https://doi.org/10.4171/jncg/506","url":null,"abstract":"Let $Asubseteq B$ be a $C^*$-inclusion. We give efficient conditions under which $A$ separates ideals in $B$, and $B$ is purely infinite if every positive element in $A$ is properly infinite in $B$. We specialise to the case when $B$ is a crossed product for an inverse semigroup action by Hilbert bimodules or a section $C^*$-algebra of a Fell bundle over an 'etale, possibly non-Hausdorff, groupoid. Then our theory works provided $B$ is the recently introduced essential crossed product and the action is essentially exact and residually aperiodic or residually topologically free. These last notions are developed in the article.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49036457","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}
{"title":"An analog of the Krein–Milman theorem for certain non-compact convex sets","authors":"G. Elliott, Zhiqiang Li, Xia Zhao","doi":"10.4171/jncg/431","DOIUrl":"https://doi.org/10.4171/jncg/431","url":null,"abstract":"","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47841303","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}
We show that every finite GK-dimensional pre-Nichols algebra for braidings of diagonal type with connected diagram of modular, supermodular or unidentified type is a quotient of the distinguished pre-Nichols algebra introduced by the first-named author, up to two exceptions. For both of these exceptional cases, we provide a pre-Nichols algebra that substitutes the distinguished one in the sense that it projects onto all finite GK-dimensional pre-Nichols algebras. We build these two substitutes as non-trivial central extensions with finite GK-dimension of the corresponding distinguished pre-Nichols algebra. We describe these algebras by generators and relations, and provide a basis. This work essentially completes the study of eminent pre-Nichols algebras of diagonal type with connected diagram and finite-dimensional Nichols algebra.
{"title":"Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type","authors":"I. Angiono, E. Campagnolo, Guillermo Sanmarco","doi":"10.4171/jncg/497","DOIUrl":"https://doi.org/10.4171/jncg/497","url":null,"abstract":"We show that every finite GK-dimensional pre-Nichols algebra for braidings of diagonal type with connected diagram of modular, supermodular or unidentified type is a quotient of the distinguished pre-Nichols algebra introduced by the first-named author, up to two exceptions. For both of these exceptional cases, we provide a pre-Nichols algebra that substitutes the distinguished one in the sense that it projects onto all finite GK-dimensional pre-Nichols algebras. We build these two substitutes as non-trivial central extensions with finite GK-dimension of the corresponding distinguished pre-Nichols algebra. We describe these algebras by generators and relations, and provide a basis. This work essentially completes the study of eminent pre-Nichols algebras of diagonal type with connected diagram and finite-dimensional Nichols algebra.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47451339","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}
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