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TORIC REFLECTION GROUPS 环面反射群
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-10-18 DOI: 10.1017/s1446788723000101
Thomas Gobet
{"title":"TORIC REFLECTION GROUPS","authors":"Thomas Gobet","doi":"10.1017/s1446788723000101","DOIUrl":"https://doi.org/10.1017/s1446788723000101","url":null,"abstract":"Abstract Several finite complex reflection groups have a braid group that is isomorphic to a torus knot group. The reflection group is obtained from the torus knot group by declaring meridians to have order k for some $kgeq 2$ , and meridians are mapped to reflections. We study all possible quotients of torus knot groups obtained by requiring meridians to have finite order. Using the theory of J -groups of Achar and Aubert [‘On rank 2 complex reflection groups’, Comm. Algebra 36 (6) (2008), 2092–2132], we show that these groups behave like (in general, infinite) complex reflection groups of rank two. The large family of ‘toric reflection groups’ that we obtain includes, among others, all finite complex reflection groups of rank two with a single conjugacy class of reflecting hyperplanes, as well as Coxeter’s truncations of the $3$ -strand braid group. We classify these toric reflection groups and explain why the corresponding torus knot group can be naturally considered as its braid group. In particular, this yields a new infinite family of reflection-like groups admitting braid groups that are Garside groups. Moreover, we show that a toric reflection group has cyclic center by showing that the quotient by the center is isomorphic to the alternating subgroup of a Coxeter group of rank three. To this end we use the fact that the center of the alternating subgroup of an irreducible, infinite Coxeter group of rank at least three is trivial. Several ingredients of the proofs are purely Coxeter-theoretic, and might be of independent interest.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823697","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
– MULTIPLIERS ON COMMUTATIVE HYPERGROUPS -交换超群上的乘数
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-10-18 DOI: 10.1017/s1446788723000125
VISHVESH KUMAR, MICHAEL RUZHANSKY
{"title":"– MULTIPLIERS ON COMMUTATIVE HYPERGROUPS","authors":"VISHVESH KUMAR, MICHAEL RUZHANSKY","doi":"10.1017/s1446788723000125","DOIUrl":"https://doi.org/10.1017/s1446788723000125","url":null,"abstract":"Abstract The main purpose of this paper is to prove Hörmander’s $L^p$ – $L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff–Young–Paley inequality for commutative hypergroups. We show the $L^p$ – $L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chébli–Trimèche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the $L^p$ – $L^q$ norms of the heat kernel for generalised radial Laplacian.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135885044","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
AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS 区间上素数定理的显式均值估计
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-09-19 DOI: 10.1017/s1446788723000113
MICHAELA CULLY-HUGILL, ADRIAN W. DUDEK
{"title":"AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS","authors":"MICHAELA CULLY-HUGILL, ADRIAN W. DUDEK","doi":"10.1017/s1446788723000113","DOIUrl":"https://doi.org/10.1017/s1446788723000113","url":null,"abstract":"Abstract This paper gives an explicit version of Selberg’s mean-value estimate for the prime number theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to short-interval results for primes and for Goldbach numbers. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32,277log ^2 y]$ for at least half the $yin [x,2x]$ for all $xgeq 2$ , and at least one Goldbach number in $(x,x+9696 log ^2 x]$ for all $xgeq 2$ .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135015074","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 GEOMETRY OF SPACELIKE MEAN CURVATURE FLOW SOLITONS IMMERSED IN A GRW SPACETIME 沉浸在GRW时空中的类空平均曲率流孤子的几何特性
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-09-15 DOI: 10.1017/s1446788723000095
HENRIQUE F. DE LIMA, WALLACE F. GOMES, MÁRCIO S. SANTOS, MARCO ANTONIO L. VELÁSQUEZ
{"title":"ON THE GEOMETRY OF SPACELIKE MEAN CURVATURE FLOW SOLITONS IMMERSED IN A GRW SPACETIME","authors":"HENRIQUE F. DE LIMA, WALLACE F. GOMES, MÁRCIO S. SANTOS, MARCO ANTONIO L. VELÁSQUEZ","doi":"10.1017/s1446788723000095","DOIUrl":"https://doi.org/10.1017/s1446788723000095","url":null,"abstract":"Abstract We investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-Itimes _{f}M^n$ , with base $Isubset mathbb R$ , Riemannian fiber $M^n$ and warping function $fin C^infty (I)$ . For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space and to obtain nonexistence results concerning these solitons. In particular, we deal with entire graphs constructed over the Riemannian fiber $M^n$ , which are spacelike mean curvature flow solitons, and we also explore the geometry of a conformal vector field to establish topological and further rigidity results for compact (without boundary) mean curvature flow solitons in a GRW spacetime. Moreover, we study the stability of spacelike mean curvature flow solitons with respect to an appropriate stability operator. Standard examples of spacelike mean curvature flow solitons in GRW spacetimes are exhibited, and applications related to these examples are given.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436865","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
JAZ volume 115 issue 2 Cover and Front matter jazz第115卷第2期封面和封面问题
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-09-11 DOI: 10.1017/s1446788722000325
{"title":"JAZ volume 115 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000325","DOIUrl":"https://doi.org/10.1017/s1446788722000325","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":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980382","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
JAZ volume 115 issue 2 Cover and Back matter jazz第115卷第2期封面和封底
4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-09-11 DOI: 10.1017/s1446788722000337
{"title":"JAZ volume 115 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000337","DOIUrl":"https://doi.org/10.1017/s1446788722000337","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":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980441","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
HALL CLASSES OF GROUPS WITH A LOCALLY FINITE OBSTRUCTION 具有局部有限阻塞的群的霍尔类
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-07-24 DOI: 10.1017/s1446788723000071
F. de Giovanni, M. Trombetti, B. Wehrfritz
{"title":"HALL CLASSES OF GROUPS WITH A LOCALLY FINITE OBSTRUCTION","authors":"F. de Giovanni, M. Trombetti, B. Wehrfritz","doi":"10.1017/s1446788723000071","DOIUrl":"https://doi.org/10.1017/s1446788723000071","url":null,"abstract":"\u0000 A well-known theorem of Philip Hall states that if a group G has a nilpotent normal subgroup N such that \u0000 \u0000 \u0000 \u0000$G/N'$\u0000\u0000 \u0000 is nilpotent, then G itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group G admitting a nilpotent normal subgroup N such that \u0000 \u0000 \u0000 \u0000$G/N'$\u0000\u0000 \u0000 belongs to 𝔛. Hall classes have been considered by several authors, such as Plotkin [‘Some properties of automorphisms of nilpotent groups’, Soviet Math. Dokl.2 (1961), 471–474] and Robinson [‘A property of the lower central series of a group’, Math. Z.107 (1968), 225–231]. A further detailed study of Hall classes is performed by us in another paper [‘Hall classes of groups’, to appear] and we also investigate the behaviour of the class of finite-by-𝔜 groups for a given Hall class 𝔜 [‘Hall classes in linear groups’, to appear]. The aim of this paper is to prove that for most natural choices of the Hall class 𝔜, also the classes \u0000 \u0000 \u0000 \u0000$(mathbf{L}mathfrak{F})mathfrak{Y}$\u0000\u0000 \u0000 and 𝔅𝔜 are Hall classes, where L𝔉 is the class of locally finite groups and 𝔅 is the class of locally finite groups of finite exponent.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88889726","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
WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS 实秩1半单李群上某些banach代数的维纳陶伯定理
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-07-18 DOI: 10.1017/s144678872300006x
Tapendu Rana
{"title":"WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS","authors":"Tapendu Rana","doi":"10.1017/s144678872300006x","DOIUrl":"https://doi.org/10.1017/s144678872300006x","url":null,"abstract":"\u0000 We prove Wiener Tauberian theorem type results for various spaces of radial functions, which are Banach algebras on a real-rank-one semisimple Lie group G. These are natural generalizations of the Wiener Tauberian theorem for the commutative Banach algebra of the integrable radial functions on G.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85815482","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
JAZ volume 115 issue 1 Cover and Back matter jazz第115卷第1期封面和封底
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-07-17 DOI: 10.1017/s1446788722000313
{"title":"JAZ volume 115 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s1446788722000313","DOIUrl":"https://doi.org/10.1017/s1446788722000313","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87960392","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
JAZ volume 115 issue 1 Cover and Front matter jazz第115卷第1期封面和封面问题
IF 0.7 4区 数学
Journal of the Australian Mathematical Society Pub Date : 2023-07-17 DOI: 10.1017/s1446788722000301
{"title":"JAZ volume 115 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788722000301","DOIUrl":"https://doi.org/10.1017/s1446788722000301","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76831243","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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