Journal of the Australian Mathematical Society最新文献

{"title":"NORMAL SUBMONOIDS AND CONGRUENCES ON A MONOID","authors":"JOSEP ELGUETA","doi":"10.1017/s1446788723000204","DOIUrl":"https://doi.org/10.1017/s1446788723000204","url":null,"abstract":"<p>A notion of <span>normal submonoid</span> of a monoid <span>M</span> is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {NorSub}(M)$</span></span></img></span></span> of normal submonoids of <span>M</span> is a complete lattice. Joins are explicitly described and the lattice is computed for the finite full transformation monoids <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$T_n$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$ngeq ~1$</span></span></img></span></span>. It is also shown that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {NorSub}(M)$</span></span></img></span></span> is modular for a specific family of commutative monoids, including all Krull monoids, and that it, as a join semilattice, embeds isomorphically onto a join subsemilattice of the lattice <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {Cong}(M)$</span></span></img></span></span> of congruences on <span>M</span>. This leads to a new strategy for computing <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {Cong}(M)$</span></span></img></span></span> consisting of computing <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231215153200057-0472:S1446788723000204:S1446788723000204_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {NorSub}(M)$</span></span></img></span></span> and the so-called unital congruences on the quotients of <span>M</span> modulo its normal submonoids. This provides a new perspective on Malcev’s computation of the congruences on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138717306","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":"BRATTELI–VERSHIKISABILITY OF POLYGONAL BILLIARDS ON THE HYPERBOLIC PLANE","authors":"ANIMA NAGAR, PRADEEP SINGH","doi":"10.1017/s1446788723000174","DOIUrl":"https://doi.org/10.1017/s1446788723000174","url":null,"abstract":"Bratteli–Vershik models of compact, invertible zero-dimensional systems have been well studied. We take up such a study for polygonal billiards on the hyperbolic plane, thus considering these models beyond zero-dimensions. We describe the associated Bratteli models and show that these billiard dynamics can be described by Vershik maps.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681885","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":"FINITELY PRESENTED INVERSE SEMIGROUPS WITH FINITELY MANY IDEMPOTENTS IN EACH -CLASS AND NON-HAUSDORFF UNIVERSAL GROUPOIDS","authors":"PEDRO V. SILVA, BENJAMIN STEINBERG","doi":"10.1017/s1446788723000198","DOIUrl":"https://doi.org/10.1017/s1446788723000198","url":null,"abstract":"<p>The complex algebra of an inverse semigroup with finitely many idempotents in each <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231212123316423-0307:S1446788723000198:S1446788723000198_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal D$</span></span></img></span></span>-class is stably finite by a result of Munn. This can be proved fairly easily using <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231212123316423-0307:S1446788723000198:S1446788723000198_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}$</span></span></img></span></span>-algebras for inverse semigroups satisfying this condition that have a Hausdorff universal groupoid, or more generally for direct limits of inverse semigroups satisfying this condition and having Hausdorff universal groupoids. It is not difficult to see that a finitely presented inverse semigroup with a non-Hausdorff universal groupoid cannot be a direct limit of inverse semigroups with Hausdorff universal groupoids. We construct here countably many nonisomorphic finitely presented inverse semigroups with finitely many idempotents in each <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231212123316423-0307:S1446788723000198:S1446788723000198_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal D$</span></span></img></span></span>-class and non-Hausdorff universal groupoids. At this time, there is not a clear <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231212123316423-0307:S1446788723000198:S1446788723000198_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}$</span></span></img></span></span>-algebraic technique to prove these inverse semigroups have stably finite complex algebras.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578897","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":"COMMON ZEROS OF IRREDUCIBLE CHARACTERS","authors":"NGUYEN N. HUNG, ALEXANDER MORETÓ, LUCIA MOROTTI","doi":"10.1017/s1446788723000216","DOIUrl":"https://doi.org/10.1017/s1446788723000216","url":null,"abstract":"<p>We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231208131534917-0583:S1446788723000216:S1446788723000216_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {S}_n$</span></span></img></span></span>, it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this phenomenon, we introduce <span>the common-zero graph</span> of a finite group <span>G</span>, with nonlinear irreducible characters of <span>G</span> as vertices, and edges connecting characters that vanish on some common group element. We show that for solvable and simple groups, the number of connected components of this graph is bounded above by three. Lastly, the result for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231208131534917-0583:S1446788723000216:S1446788723000216_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf {S}_n$</span></span></img></span></span> is applied to prove the nonequivalence of the metrics on permutations induced from faithful irreducible characters of the group.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138569372","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":"RODRIGUES FORMULA AND LINEAR INDEPENDENCE FOR VALUES OF HYPERGEOMETRIC FUNCTIONS WITH VARYING PARAMETERS","authors":"MAKOTO KAWASHIMA","doi":"10.1017/s1446788723000186","DOIUrl":"https://doi.org/10.1017/s1446788723000186","url":null,"abstract":"In this article, we prove a generalized Rodrigues formula for a wide class of holonomic Laurent series, which yields a new linear independence criterion concerning their values at algebraic points. This generalization yields a new construction of Padé approximations including those for Gauss hypergeometric functions. In particular, we obtain a linear independence criterion over a number field concerning values of Gauss hypergeometric functions, allowing <jats:italic>the parameters of Gauss hypergeometric functions to vary.</jats:italic>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531150","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":"JAZ volume 115 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000349","DOIUrl":"https://doi.org/10.1017/s1446788722000349","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135242710","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":"JAZ volume 115 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000350","DOIUrl":"https://doi.org/10.1017/s1446788722000350","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135242708","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":"INDEX","authors":"","doi":"10.1017/s1446788722000362","DOIUrl":"https://doi.org/10.1017/s1446788722000362","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139282345","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":"SOME GLOBAL EXISTENCE RESULTS ON LOCALLY FINITE GRAPHS","authors":"SHOUDONG MAN, GUOQING ZHANG","doi":"10.1017/s1446788723000149","DOIUrl":"https://doi.org/10.1017/s1446788723000149","url":null,"abstract":"Abstract Let $G=(V, E)$ be a locally finite graph with the vertex set V and the edge set E , where both V and E are infinite sets. By dividing the graph G into a sequence of finite subgraphs, the existence of a sequence of local solutions to several equations involving the p -Laplacian and the poly-Laplacian systems is confirmed on each subgraph, and the global existence for each equation on graph G is derived by the convergence of these local solutions. Such results extend the recent work of Grigor’yan, Lin and Yang [ J. Differential Equations , 261 (2016), 4924–4943; Rev. Mat. Complut. , 35 (2022), 791–813]. The method in this paper also provides an idea for investigating similar problems on infinite graphs.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636457","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":"FAITHFULNESS OF THE 2-BRAID GROUP VIA ZIGZAG ALGEBRA IN TYPE B","authors":"EDMUND HENG, KIE SENG NGE","doi":"10.1017/s1446788723000137","DOIUrl":"https://doi.org/10.1017/s1446788723000137","url":null,"abstract":"Abstract We show that a certain category of bimodules over a finite-dimensional quiver algebra known as a type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier’s conjecture on the faithfulness of the 2-braid groups for type B .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235258","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}