Journal of the Australian Mathematical Society最新文献

{"title":"RADU GROUPS ACTING ON TREES ARE CCR","authors":"LANCELOT SEMAL","doi":"10.1017/s1446788723000381","DOIUrl":"https://doi.org/10.1017/s1446788723000381","url":null,"abstract":"<p>We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$2$</span></span></img></span></span>-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(d_0,d_1)$</span></span></img></span></span>-semi-regular trees such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$d_0,d_1in Theta $</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$Theta $</span></span></img></span></span> is an asymptotically dense set of positive integers.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047484","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":"THE -GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS","authors":"MARCO ANTONIO PELLEGRINI, MARIA CHIARA TAMBURINI BELLANI","doi":"10.1017/s1446788724000016","DOIUrl":"https://doi.org/10.1017/s1446788724000016","url":null,"abstract":"The complete classification of the finite simple groups that are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline2.png\" /> <jats:tex-math> $(2,3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generated is a problem which is still open only for orthogonal groups. Here, we construct <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline3.png\" /> <jats:tex-math> $(2, 3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generators for the finite odd-dimensional orthogonal groups <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline4.png\" /> <jats:tex-math> $Omega _{2k+1}(q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline5.png\" /> <jats:tex-math> $kgeq 4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. As a byproduct, we also obtain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline6.png\" /> <jats:tex-math> $(2,3)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generators for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline7.png\" /> <jats:tex-math> $Omega _{4k}^+(q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline8.png\" /> <jats:tex-math> $kgeq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:italic>q</jats:italic> odd, and for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline9.png\" /> <jats:tex-math> $Omega _{4k+2}^pm (q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline10.png\" /> <jats:tex-math> $kgeq 4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000016_inline11.png\" /> <jats:tex-math> $qequiv pm 1~ mathrm {(mod~ 4)}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"119 50 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002580","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 ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS","authors":"JIE DING, JIANHUA ZHENG","doi":"10.1017/s1446788723000393","DOIUrl":"https://doi.org/10.1017/s1446788723000393","url":null,"abstract":"This paper consists of two parts. The first is to study the existence of a point <jats:italic>a</jats:italic> at the intersection of the Julia set and the escaping set such that <jats:italic>a</jats:italic> goes to infinity under iterates along Julia directions or Borel directions. Additionally, we find such points that approximate all Borel directions to escape if the meromorphic functions have positive lower order. We confirm the existence of such slowly escaping points under a weaker growth condition. The second is to study the connection between the Fatou set and argument distribution. In view of the filling disks, we show nonexistence of multiply connected Fatou components if an entire function satisfies a weaker growth condition. We prove that the absence of singular directions implies the nonexistence of large annuli in the Fatou set.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"53 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768268","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":"THE RIEFFEL CORRESPONDENCE FOR EQUIVALENT FELL BUNDLES","authors":"S. KALISZEWSKI, JOHN QUIGG, DANA P. WILLIAMS","doi":"10.1017/s144678872300037x","DOIUrl":"https://doi.org/10.1017/s144678872300037x","url":null,"abstract":"<p>We establish a generalized Rieffel correspondence for ideals in equivalent Fell bundles.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482754","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 WEIGHTED ESTIMATE OF COMMUTATORS OF BOCHNER–RIESZ OPERATORS FOR HERMITE OPERATOR","authors":"PENG CHEN, XIXI LIN","doi":"10.1017/s1446788723000368","DOIUrl":"https://doi.org/10.1017/s1446788723000368","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;H&lt;/span&gt; be the Hermite operator &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$-Delta +|x|^2$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; on &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathbb {R}^n$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. We prove a weighted &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$L^2$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; estimate of the maximal commutator operator &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline5.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$sup _{R&gt;0}|[b, S_R^lambda (H)](f)|$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, where &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline6.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$ [b, S_R^lambda (H)](f) = bS_R^lambda (H) f - S_R^lambda (H)(bf) $&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; is the commutator of a BMO function &lt;span&gt;b&lt;/span&gt; and the Bochner–Riesz means &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline7.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$S_R^lambda (H)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; for the Hermite operator &lt;span&gt;H&lt;/span&gt;. As an application, we obtain the almost everywhere convergence of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline8.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$[b, S_R^lambda (H)](f)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; for large &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline9.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$lambda $&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; and &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240114040524355-0595:S1446788723000368:S1446788723000368_inline10.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$fin","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139468895","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":"THE PRO--SOLVABLE TOPOLOGY ON A FREE GROUP","authors":"Claude Marion, P. V. Silva, Gareth Tracey","doi":"10.1017/s1446788723000162","DOIUrl":"https://doi.org/10.1017/s1446788723000162","url":null,"abstract":"\u0000 We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro-\u0000 \u0000 \u0000 \u0000$mathbf {V}$\u0000\u0000 \u0000 topology when \u0000 \u0000 \u0000 \u0000$mathbf {V}$\u0000\u0000 \u0000 is an equational pseudovariety of finite groups, such as the pseudovariety \u0000 \u0000 \u0000 \u0000$mathbf {S}_k$\u0000\u0000 \u0000 of all finite solvable groups with derived length \u0000 \u0000 \u0000 \u0000$leq k$\u0000\u0000 \u0000 . We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"42 32","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946488","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":"QUALITATIVE UNCERTAINTY PRINCIPLE ON CERTAIN LIE GROUPS","authors":"ARUP CHATTOPADHYAY, DEBKUMAR GIRI, R. K. SRIVASTAVA","doi":"10.1017/s1446788723000150","DOIUrl":"https://doi.org/10.1017/s1446788723000150","url":null,"abstract":"<p>In this article, we study the recent development of the qualitative uncertainty principle on certain Lie groups. In particular, we consider that if the Weyl transform on certain step-two nilpotent Lie groups is of finite rank, then the function has to be zero almost everywhere as long as the nonvanishing set for the function has finite measure. Further, we consider that if the Weyl transform of each Fourier–Wigner piece of a suitable function on the Heisenberg motion group is of finite rank, then the function has to be zero almost everywhere whenever the nonvanishing set for each Fourier–Wigner piece has finite measure.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"116 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138716298","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":"NORMAL SUBMONOIDS AND CONGRUENCES ON A MONOID","authors":"JOSEP ELGUETA","doi":"10.1017/s1446788723000204","DOIUrl":"https://doi.org/10.1017/s1446788723000204","url":null,"abstract":"&lt;p&gt;A notion of &lt;span&gt;normal submonoid&lt;/span&gt; of a monoid &lt;span&gt;M&lt;/span&gt; is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathsf {NorSub}(M)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; of normal submonoids of &lt;span&gt;M&lt;/span&gt; is a complete lattice. Joins are explicitly described and the lattice is computed for the finite full transformation monoids &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$T_n$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$ngeq ~1$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. It is also shown that &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathsf {NorSub}(M)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; 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 &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathsf {Cong}(M)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; of congruences on &lt;span&gt;M&lt;/span&gt;. This leads to a new strategy for computing &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathsf {Cong}(M)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; consisting of computing &lt;span&gt;&lt;span&gt;&lt;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\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathsf {NorSub}(M)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; and the so-called unital congruences on the quotients of &lt;span&gt;M&lt;/span&gt; modulo its normal submonoids. This provides a new perspective on Malcev’s computation of the congruences on &lt;span&gt;&lt;span&gt;&lt;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":"69 1","pages":""},"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":"12 1","pages":""},"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":"42 Pt B 1","pages":""},"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}