We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if and only if it is a partial quasimorphism bounded on a generating set. We also show that an undistorted element is always detected by an antisymmetric homogeneo
{"title":"On Lipschitz functions on groups equipped with conjugation-invariant norms","authors":"Jarek Kędra","doi":"10.4064/cm9173-8-2023","DOIUrl":"https://doi.org/10.4064/cm9173-8-2023","url":null,"abstract":"We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if and only if it is a partial quasimorphism bounded on a generating set. We also show that an undistorted element is always detected by an antisymmetric homogeneo","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$ast $-Homomorphisms of matrix algebras\u0000over pseudo-solenoids\u0000that are approximated by $ast $-isomorphisms","authors":"K. Kawamura","doi":"10.4064/cm8862-2-2023","DOIUrl":"https://doi.org/10.4064/cm8862-2-2023","url":null,"abstract":"","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70144157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junpeng Wang, Gang Yang, Qingyu Shao, Xiaoxiang Zhang
It is well-known that the weak global dimension of a ring does not exceed its global dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for coherent rings. We extend this result to an arbitrary ring. As applications, we ch
{"title":"On Gorenstein global and Gorenstein weak global dimensions","authors":"Junpeng Wang, Gang Yang, Qingyu Shao, Xiaoxiang Zhang","doi":"10.4064/cm9052-7-2023","DOIUrl":"https://doi.org/10.4064/cm9052-7-2023","url":null,"abstract":"It is well-known that the weak global dimension of a ring does not exceed its global dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for coherent rings. We extend this result to an arbitrary ring. As applications, we ch","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"161 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135839241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new criterion for solvability of a finite group by the sum of orders of non-normal subgroups","authors":"Liang Cui, Wei Meng, Jiakuan Lu, Weicheng Zheng","doi":"10.4064/cm9175-10-2023","DOIUrl":"https://doi.org/10.4064/cm9175-10-2023","url":null,"abstract":"","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135316849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that if a non-cosymplectic almost cosymplectic $(kappa ,mu )$-manifold of dimension 3 admits a conformal vector field, then the vector field is necessarily Killing.
{"title":"Conformal vector fields on almost cosymplectic 3-manifolds","authors":"Wenjie Wang","doi":"10.4064/cm8911-7-2023","DOIUrl":"https://doi.org/10.4064/cm8911-7-2023","url":null,"abstract":"We prove that if a non-cosymplectic almost cosymplectic $(kappa ,mu )$-manifold of dimension 3 admits a conformal vector field, then the vector field is necessarily Killing.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135839500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove Kaneko–Ohno’s duality relation for multiple zeta star values by using an integral involving the classical polylogarithm function and logarithmic function with the help of a few results of Xu (2017). Moreover, we also discuss some related results
{"title":"Another proof of Kaneko–Ohno’s duality formula for multiple zeta star values","authors":"Xin Si, Fan Luo","doi":"10.4064/cm8943-5-2023","DOIUrl":"https://doi.org/10.4064/cm8943-5-2023","url":null,"abstract":"We prove Kaneko–Ohno’s duality relation for multiple zeta star values by using an integral involving the classical polylogarithm function and logarithmic function with the help of a few results of Xu (2017). Moreover, we also discuss some related results","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135562580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study an $m$-quasi-Einstein manifold $(M,g,f,lambda )$ with finite $m$, and a non-homothetic conformal vector field $U$ that leaves the potential vector field and the scalar curvature both invariant, and show that either $M$ is trivial, or $U$ is Kill
{"title":"Quasi-Einstein manifolds admitting conformal vector fields","authors":"Rahul Poddar, S. Balasubramanian, Ramesh Sharma","doi":"10.4064/cm8903-6-2023","DOIUrl":"https://doi.org/10.4064/cm8903-6-2023","url":null,"abstract":"We study an $m$-quasi-Einstein manifold $(M,g,f,lambda )$ with finite $m$, and a non-homothetic conformal vector field $U$ that leaves the potential vector field and the scalar curvature both invariant, and show that either $M$ is trivial, or $U$ is Kill","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135957713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish an optimal integral inequality for closed hypersurfaces in the odd-dimensional unit sphere $mathbb S^{2n+1}(1)$ with vanishing Reeb function that involves the shape operator $A$ and the contact vector field $U$. The integral inequality is op
{"title":"A rigidity theorem for hypersurfaces of the odd-dimensional unit sphere $mathbb S^{2n+1}(1)$","authors":"Mingzhu Gao, Zejun Hu, Cheng Xing","doi":"10.4064/cm8966-7-2023","DOIUrl":"https://doi.org/10.4064/cm8966-7-2023","url":null,"abstract":"We establish an optimal integral inequality for closed hypersurfaces in the odd-dimensional unit sphere $mathbb S^{2n+1}(1)$ with vanishing Reeb function that involves the shape operator $A$ and the contact vector field $U$. The integral inequality is op","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136203436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the structure of metabelian Galois coverings of complex algebraic varieties","authors":"Abolfazl Mohajer","doi":"10.4064/cm8582-2-2022","DOIUrl":"https://doi.org/10.4064/cm8582-2-2022","url":null,"abstract":"","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70141102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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