International Journal of Mathematics最新文献

{"title":"Distance formulas in Bruhat–Tits building of SLd(ℚp)","authors":"Dominik Lachman","doi":"10.1142/s0129167x24500058","DOIUrl":"https://doi.org/10.1142/s0129167x24500058","url":null,"abstract":"<p>We study the distance on the Bruhat–Tits building of the group <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy=\"false\">(</mo><msub><mrow><mi>ℚ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> (and its other combinatorial properties). Coding its vertices by certain matrix representatives, we introduce a way how to build formulas with combinatorial meanings. In Theorem 1, we give an explicit formula for the graph distance <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>δ</mi><mo stretchy=\"false\">(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of two vertices <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> and <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>β</mi></math></span><span></span> (without having to specify their common apartment). Our main result, Theorem 2, then extends the distance formula to a formula for the smallest total distance of a vertex from a given finite set of vertices. In the appendix we consider the case of <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">(</mo><msub><mrow><mi>ℚ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> and give a formula for the number of edges shared by two given apartments.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154654","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":"Properly outer and strictly outer actions of finite groups on prime C*-algebras","authors":"Costel Peligrad","doi":"10.1142/s0129167x24500071","DOIUrl":"https://doi.org/10.1142/s0129167x24500071","url":null,"abstract":"<p>An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper, I define the notion of strictly outer action (similar to the definition for von Neumann factors in [S. Vaes, The unitary implementation of a locally compact group action, <i>J. Funct. Anal.</i><b>180</b> (2001) 426–480]) and prove that for finite groups and prime C*-algebras, it is equivalent to the proper outerness of the action. For finite abelian groups this is equivalent to other relevant properties of the action.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154911","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 uniqueness of submaximally symmetric parabolic geometries","authors":"Dennis The","doi":"10.1142/s0129167x24400019","DOIUrl":"https://doi.org/10.1142/s0129167x24400019","url":null,"abstract":"<p>Among the (regular, normal) parabolic geometries of type <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mi>P</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, there is a locally unique maximally symmetric structure and it has the symmetry dimension <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">dim</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> is a complex or split-real simple Lie group of rank at least three or when <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mi>P</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo stretchy=\"false\">(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span>, we establish a local uniqueness result for submaximally symmetric structures of type <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>G</mi><mo>,</mo><mi>P</mi><mo stretchy=\"false\">)</mo></math></span><span></span>.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154570","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":"Kawaguchi–Silverman conjecture on automorphisms of projective threefolds","authors":"Sichen Li","doi":"10.1142/s0129167x24500022","DOIUrl":"https://doi.org/10.1142/s0129167x24500022","url":null,"abstract":"<p>Under the framework of dynamics on normal projective varieties by Kawamata, Nakayama and Zhang, and Hu and Li, we may reduce Kawaguchi–Silverman conjecture for automorphisms <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi></math></span><span></span> on normal projective threefolds <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> with either the canonical divisor <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span><span></span> is trivial or negative Kodaira dimension to the following two cases: (i) <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi></math></span><span></span> is a primitively automorphism of a weak Calabi–Yau threefold, (ii) <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> is a rationally connected threefold. And we prove Kawaguchi–Silverman conjecture is true for automorphisms of normal projective varieties <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> with the irregularity <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi><mo stretchy=\"false\">(</mo><mi>X</mi><mo stretchy=\"false\">)</mo><mo>≥</mo><mstyle><mtext mathvariant=\"normal\">dim</mtext></mstyle><mi>X</mi><mo stretchy=\"false\">−</mo><mn>1</mn></math></span><span></span>. Finally, we discuss Kawaguchi–Silverman conjecture on normal projective varieties with Picard number two.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"80 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154656","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":"Vector invariants of permutation groups in characteristic zero","authors":"Fabian Reimers, Müfit Sezer","doi":"10.1142/s0129167x23501112","DOIUrl":"https://doi.org/10.1142/s0129167x23501112","url":null,"abstract":"<p>We consider a finite permutation group acting naturally on a vector space <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>V</mi></math></span><span></span> over a field <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo></math></span><span></span>. A well-known theorem of Göbel asserts that the corresponding ring of invariants <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo><msup><mrow><mo stretchy=\"false\">[</mo><mi>V</mi><mo stretchy=\"false\">]</mo></mrow><mrow><mi>G</mi></mrow></msup></math></span><span></span> is generated by the invariants of degree at most <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mfenced close=\")\" open=\"(\" separators=\"\"><mfrac linethickness=\"0.0pt\"><mrow><mo>dim</mo><mi>V</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mfenced></math></span><span></span>. In this paper, we show that if the characteristic of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo></math></span><span></span> is zero, then the top degree of vector coinvariants <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo><msub><mrow><mo stretchy=\"false\">[</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msup><mo stretchy=\"false\">]</mo></mrow><mrow><mi>G</mi></mrow></msub></math></span><span></span> is also bounded above by <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mfenced close=\")\" open=\"(\" separators=\"\"><mfrac linethickness=\"0.0pt\"><mrow><mstyle><mtext mathvariant=\"normal\">dim</mtext></mstyle><mi>V</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mfenced></math></span><span></span>, which implies the degree bound <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mfenced close=\")\" open=\"(\" separators=\"\"><mfrac linethickness=\"0.0pt\"><mrow><mo>dim</mo><mi>V</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mfenced><mo stretchy=\"false\">+</mo><mn>1</mn></math></span><span></span> for the ring of vector invariants <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mo>𝕜</mo><msup><mrow><mo stretchy=\"false\">[</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msup><mo stretchy=\"false\">]</mo></mrow><mrow><mi>G</mi></mrow></msup></math></span><span></span>. So, Göbel’s bound almost holds for vector invariants in characteristic zero as well.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154908","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":"Modular Categories of Frobenius-Perron Dimension p2q2r2 and Perfect Modular Categories","authors":"Dewei Zhou, Jingcheng Dong","doi":"10.1142/s0129167x24500010","DOIUrl":"https://doi.org/10.1142/s0129167x24500010","url":null,"abstract":"","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"74 8","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138999717","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":"Contact Non-Squeezing and Orderability via the Shape Invariant","authors":"Dylan Cant","doi":"10.1142/s0129167x23501094","DOIUrl":"https://doi.org/10.1142/s0129167x23501094","url":null,"abstract":"We prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain manifolds. The class of embeddings includes embeddings which are not isotopic to the identity. This yields a new proof that there is no positive loop of contactomorphisms in the unit cotangent bundles under consideration. The proof uses the shape invariant introduced by Sikorav and Eliashberg.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":" October","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186153","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":"Complex vs Convex Morse Functions and Geodesic Open Books","authors":"Pierre Dehornoy, Burak Ozbagci","doi":"10.1142/s0129167x23501100","DOIUrl":"https://doi.org/10.1142/s0129167x23501100","url":null,"abstract":"Suppose that $Sigma$ is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are four seemingly distinct constructions of open books on the unit (co)tangent bundle of $Sigma$, having complex, symplectic, contact, and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on $Sigma$. We show that the resulting open books are pairwise isomorphic provided that the ordered Morse function is adapted to the admissible divide on $Sigma$. Moreover, we observe that if $Sigma$ has positive genus, then none of these open books are planar and furthermore, we determine the only cases when they have genus one pages.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"84 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087570","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 Second Main Theorem of Finite Ramified Coverings","authors":"Giang Le","doi":"10.1142/s0129167x23500969","DOIUrl":"https://doi.org/10.1142/s0129167x23500969","url":null,"abstract":"In this paper, we study a second main theorem for holomorphic curves from finite ramified coverings of the complex line to complex projective varieties intersecting hypersurfaces in subgeneral position.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":" 22","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293377","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 Supersingular Locus of the Shimura Variety for GU(2,2) over a Ramified Prime","authors":"Yasuhiro Oki","doi":"10.1142/s0129167x23500945","DOIUrl":"https://doi.org/10.1142/s0129167x23500945","url":null,"abstract":"We study the structure of the supersingular locus of the Rapoport–Zink integral model of the Shimura variety for GU(2,2) over a ramified odd prime with the special maximal parahoric level. We prove that the supersingular locus equals the disjoint union of two basic loci, one of which is contained in the flat locus, and the other is not. We also describe explicitly the structure of the basic loci. More precisely, the former one is purely 2-dimensional, and each irreducible component is birational to the Fermat surface. On the other hand, the latter one is purely [Formula: see text]-dimensional, and each irreducible component is birational to the projective line.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"27 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":"135432004","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}