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On the equivalence between the existence of n-kernels and n-cokernels 关于n核的存在性与n核的等价性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-04-17 DOI: 10.1007/s00013-026-02238-x
Vitor Gulisz, Wolfgang Rump
{"title":"On the equivalence between the existence of n-kernels and n-cokernels","authors":"Vitor Gulisz,&nbsp;Wolfgang Rump","doi":"10.1007/s00013-026-02238-x","DOIUrl":"10.1007/s00013-026-02238-x","url":null,"abstract":"<div><p>We give an elementary proof of the statement that if an idempotent complete preadditive category has weak kernels and weak cokernels, then it has <i>n</i>-kernels if and only if it has <i>n</i>-cokernels, where <i>n</i> is a nonnegative integer. As a consequence, elementary proofs of two results concerning the equality between the global dimensions of certain right and left module categories are obtained.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"493 - 499"},"PeriodicalIF":0.5,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02238-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasikernels and kernels of irreducible characters 拟核和不可约字符核
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-04-16 DOI: 10.1007/s00013-026-02226-1
Pujin Li, Haipeng Qu
{"title":"Quasikernels and kernels of irreducible characters","authors":"Pujin Li,&nbsp;Haipeng Qu","doi":"10.1007/s00013-026-02226-1","DOIUrl":"10.1007/s00013-026-02226-1","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group, and <span>(chi )</span> be an irreducible complex character of <i>G</i>. In this note, we define <span>(textrm{zk}(G)=|{ chi in textrm{Irr}(G) bigm |textrm{Z}(chi )=textrm{Ker}(chi ) }|)</span>. We prove that <span>(textrm{zk}(G)=1)</span> if and only if <i>G</i> is nilpotent, which provides a new criterion for nilpotency. We also show that <i>G</i> is solvable when <span>(textrm{zk}(G)leqslant 4)</span> and characterize non-solvable groups with <span>(textrm{zk}(G)=5)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"453 - 459"},"PeriodicalIF":0.5,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968111","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}
引用次数: 0
Spectral partition of connected graphs by resistance Laplacian matrices 用阻力拉普拉斯矩阵划分连通图的谱
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-04-07 DOI: 10.1007/s00013-026-02247-w
Vinayak Gupta, Gargi Lather, R. Balaji
{"title":"Spectral partition of connected graphs by resistance Laplacian matrices","authors":"Vinayak Gupta,&nbsp;Gargi Lather,&nbsp;R. Balaji","doi":"10.1007/s00013-026-02247-w","DOIUrl":"10.1007/s00013-026-02247-w","url":null,"abstract":"<div><p>Let <i>G</i> be a connected graph on <i>n</i> vertices with weights assigned to each of its edges. If <span>(R=(r_{ij}))</span> is the resistance matrix of <i>G</i>, then the resistance Laplacian of <i>G</i> is </p><div><div><span>$$begin{aligned} {widetilde{R}}:=textrm{Diag}left( sum _{j=1}^nr_{1j},dotsc ,sum _{j=1}^{n} r_{nj}right) -R. end{aligned}$$</span></div></div><p>Let <span>((x_1,dotsc ,x_n)')</span> be an eigenvector corresponding to the largest eigenvalue of <span>({widetilde{R}})</span>. In this paper, we establish that the subgraphs induced by <span>({j: x_j ge 0})</span> and <span>({j:x_j le 0})</span> are connected components of <i>G</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"483 - 491"},"PeriodicalIF":0.5,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968088","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}
引用次数: 0
On the nonexistence of a Green functor with values (hbox {spin}^c) bordism and spin bordism 值为(hbox {spin}^c)和自旋的Green函子的不存在性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-29 DOI: 10.1007/s00013-026-02229-y
Hassan H. Abdallah, Zachary Halladay, Yigal Kamel
{"title":"On the nonexistence of a Green functor with values (hbox {spin}^c) bordism and spin bordism","authors":"Hassan H. Abdallah,&nbsp;Zachary Halladay,&nbsp;Yigal Kamel","doi":"10.1007/s00013-026-02229-y","DOIUrl":"10.1007/s00013-026-02229-y","url":null,"abstract":"<div><p>We show that there does not exist a <span>(C_2)</span>-ring spectrum whose underlying ring spectrum is <span>(textrm{MSpin}^c)</span> and whose <span>(C_2)</span>-fixed point spectrum is <span>(textrm{MSpin})</span>. As a corollary, the <span>(hbox {spin}^c)</span> and spin orientations of Atiyah–Bott–Shapiro cannot be obtained as the underlying and fixed point maps of a single map of <span>(C_2)</span>-ring spectra.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"377 - 381"},"PeriodicalIF":0.5,"publicationDate":"2026-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02229-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A parity phenomenon of spherical tilings 球面平铺的宇称现象
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-27 DOI: 10.1007/s00013-026-02233-2
Hoi Ping Luk
{"title":"A parity phenomenon of spherical tilings","authors":"Hoi Ping Luk","doi":"10.1007/s00013-026-02233-2","DOIUrl":"10.1007/s00013-026-02233-2","url":null,"abstract":"<div><p>Can the sphere be tiled by an odd number of congruent polygons in an edge-to-edge arrangement? The answer is negative under a natural setting where polygons have at least 3 edges and at least 3 polygons meet at each vertex. The parity phenomenon has come to light after a voluminous classification of spherical tilings. We offer a short proof of it and draw a parallel to a result in polyhedra by Branko Grünbaum.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"541 - 550"},"PeriodicalIF":0.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02233-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Liouville-type theorem for subharmonic functions and its applications to quasi-Einstein manifolds 次调和函数的liouville型定理及其在拟爱因斯坦流形中的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-25 DOI: 10.1007/s00013-026-02231-4
Rahul Poddar
{"title":"A Liouville-type theorem for subharmonic functions and its applications to quasi-Einstein manifolds","authors":"Rahul Poddar","doi":"10.1007/s00013-026-02231-4","DOIUrl":"10.1007/s00013-026-02231-4","url":null,"abstract":"<div><p>We prove a Liouville-type theorem for subharmonic functions by assuming a finite weighted Dirichlet integral condition, and then apply it to study the rigidity of complete, non-compact <i>m</i>-quasi-Einstein manifolds. Further, we obtain the triviality of a complete, non-compact <i>m</i>-quasi-Einstein manifold <i>M</i> by imposing certain regularity conditions on the potential function and Ricci curvature constraints on <i>M</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"433 - 441"},"PeriodicalIF":0.5,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636895","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}
引用次数: 0
Complete quasi-Yamabe gradient solitons with bounded scalar curvature 具有有界标量曲率的完全拟雅贝梯度孤子
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-24 DOI: 10.1007/s00013-026-02236-z
Shun Maeta
{"title":"Complete quasi-Yamabe gradient solitons with bounded scalar curvature","authors":"Shun Maeta","doi":"10.1007/s00013-026-02236-z","DOIUrl":"10.1007/s00013-026-02236-z","url":null,"abstract":"<div><p>In this paper, we study complete, nontrivial quasi-Yamabe gradient solitons and obtain partial classification results under natural scalar curvature bounds. Assuming that the scalar curvature is bounded from below or above by the soliton constant, we reduce the problem to a one-dimensional ordinary differential equation and derive several rigidity results. For shrinking and steady solitons with scalar curvature strictly larger than the soliton constant and a positive coefficient of the gradient term, we prove rotational symmetry, whereas for expanding and steady solitons with scalar curvature strictly smaller than the soliton constant and a negative coefficient, we obtain explicit warped-product models whose behavior at infinity is completely determined.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"443 - 451"},"PeriodicalIF":0.5,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636892","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}
引用次数: 0
Totally disconnected semigroup compactifications: non-introversion of the full Boolean algebra of clopen sets 完全不连通半群紧化：闭集的满布尔代数的非内向性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-24 DOI: 10.1007/s00013-026-02237-y
Joshua Basman Monterrubio, Thomas Czyzowicz, Ross Stokke, Emily Thevenot
{"title":"Totally disconnected semigroup compactifications: non-introversion of the full Boolean algebra of clopen sets","authors":"Joshua Basman Monterrubio,&nbsp;Thomas Czyzowicz,&nbsp;Ross Stokke,&nbsp;Emily Thevenot","doi":"10.1007/s00013-026-02237-y","DOIUrl":"10.1007/s00013-026-02237-y","url":null,"abstract":"<div><p>In terms of the existence of a single clopen set and two related nets, we characterize when the full Boolean algebra <span>({mathfrak {B}}(G))</span> of clopen subsets of a topological group <i>G</i> is left introverted. We employ this characterization to show that when <i>G</i> is a first countable, <span>(sigma )</span>-compact, totally disconnected locally compact group, <span>({mathfrak {B}}(G))</span> is left introverted if and only if <i>G</i> is compact or discrete, thus providing a strong positive answer to a question posed in Stephens and Stokke (Q J Math 74:301–326 2023). Examples of clopen sets and nets witnessing our non-introversion theorem are presented. Some hereditary properties of left introversion of <span>({mathfrak {B}}(G))</span> are proved and then employed to extend our main result to other classes of topological groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"505 - 512"},"PeriodicalIF":0.5,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968149","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}
引用次数: 0
On the commutativity of the Berezin transform 关于Berezin变换的交换性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-23 DOI: 10.1007/s00013-026-02222-5
Alexander Borichev, Gérard Fantolini, El-Hassan Youssfi
{"title":"On the commutativity of the Berezin transform","authors":"Alexander Borichev,&nbsp;Gérard Fantolini,&nbsp;El-Hassan Youssfi","doi":"10.1007/s00013-026-02222-5","DOIUrl":"10.1007/s00013-026-02222-5","url":null,"abstract":"<div><p>We consider the commutativity problem for the Berezin transform on weighted Fock spaces. Given a real number <span>(m&gt;0)</span>, for every <span>(alpha &gt;0)</span>, we denote by <span>(B_{alpha })</span> the Berezin transform associated to the measure <span>(mu _{alpha ,m})</span> with density proportional to <span>(e^{-alpha |z|^m})</span> with respect to the Lebesgue measure on the complex plane and normalized so that <span>(mu _{alpha ,m})</span>. We show that the commutativity relation <span>(B_{alpha }B_{beta }f=B_{beta }B_{alpha }f)</span> holds for all <span>(fin L^{infty }(mathbb {C}))</span> and <span>(alpha ,beta &gt; 0)</span> if and only if <span>(m=2)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"397 - 405"},"PeriodicalIF":0.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636890","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}
引用次数: 0
Hamiltonian linking and symplectic packing 哈密顿连接与辛填充
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-19 DOI: 10.1007/s00013-026-02228-z
Dylan Cant
{"title":"Hamiltonian linking and symplectic packing","authors":"Dylan Cant","doi":"10.1007/s00013-026-02228-z","DOIUrl":"10.1007/s00013-026-02228-z","url":null,"abstract":"<div><p>In this short note, we make an observation relating symplectic packings of the standard symplectic ball by two sets and Hamiltonian linking.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"513 - 525"},"PeriodicalIF":0.5,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968185","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}
引用次数: 0
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