Proceedings of the American Mathematical Society最新文献

{"title":"Group coactions on two-dimensional Artin-Schelter regular algebras","authors":"Simon Crawford","doi":"10.1090/proc/16844","DOIUrl":"https://doi.org/10.1090/proc/16844","url":null,"abstract":"<p>We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Retraction notice","authors":"Khadime Salame","doi":"10.1090/proc/16856","DOIUrl":"https://doi.org/10.1090/proc/16856","url":null,"abstract":"","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"61 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}","authors":"Hidenori Katsurada, Henry Kim","doi":"10.1090/proc/16866","DOIUrl":"https://doi.org/10.1090/proc/16866","url":null,"abstract":"<p>In this paper, we show that the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript 7 comma 3\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=\"application/x-tex\">E_{7,3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acts is an ordinary modular form for a congruence subgroup.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods","authors":"Daoqiang Liu","doi":"10.1090/proc/16869","DOIUrl":"https://doi.org/10.1090/proc/16869","url":null,"abstract":"<p>The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Wandering domains with nearly bounded orbits","authors":"Leticia Pardo-Simón, David Sixsmith","doi":"10.1090/proc/16846","DOIUrl":"https://doi.org/10.1090/proc/16846","url":null,"abstract":"<p>In this paper we construct a bounded wandering domain with the property that, in a sense we make precise, nearly all of its forward iterates are contained within a bounded domain.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An area theorem for harmonic mappings with nonzero pole having quasiconformal extensions","authors":"Bappaditya Bhowmik, Goutam Satpati","doi":"10.1090/proc/16850","DOIUrl":"https://doi.org/10.1090/proc/16850","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma Subscript upper H Superscript k Baseline left-parenthesis p right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:mi>H</mml:mi> <mml:mi>k</mml:mi> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Sigma _H^k(p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the class of sense-preserving univalent harmonic mappings defined on the open unit disk <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper D\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"double-struck\">D</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {D}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the complex plane with a simple pole at <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"z equals p element-of left-parenthesis 0 comma 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">z=p in (0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that have <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-quasiconformal extensions (<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0 less-than-or-equal-to k greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>k</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">0leq k&gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Actions of finitely generated groups on compact metric spaces","authors":"Ursula Hamenstädt","doi":"10.1090/proc/16865","DOIUrl":"https://doi.org/10.1090/proc/16865","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated group which admits an action by homeomorphisms on a metrizable space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that there is a metric on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the 𝑝-rank of curves","authors":"Sadik Terzİ","doi":"10.1090/proc/16841","DOIUrl":"https://doi.org/10.1090/proc/16841","url":null,"abstract":"<p>In this paper, we are concerned with the computations of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rank of curves in two different setups. We first work with complete intersection varieties in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper P Superscript n Baseline for n greater-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"bold\">P</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mtext> for </mml:mtext> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbf {P}^n text { for } nge 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and compute explicitly the action of Frobenius on the top cohomology group. In case of curves and surfaces, this information suffices to determine if the variety is ordinary. Next, we consider curves on more general surfaces with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p Subscript g Baseline left-parenthesis upper S right-parenthesis equals 0 equals q left-parenthesis upper S right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>=</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p_g(S) = 0 = q(S)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such as Hirzebruch surfaces and determine <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rank of curves on Hirzebruch surfaces.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universal convexity and range problems of shifted hypergeometric functions","authors":"Toshiyuki Sugawa, Li-Mei Wang, Chengfa Wu","doi":"10.1090/proc/16849","DOIUrl":"https://doi.org/10.1090/proc/16849","url":null,"abstract":"&lt;p&gt;In the present paper, we study the shifted hypergeometric function &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis z right-parenthesis equals z 2 upper F 1 left-parenthesis a comma b semicolon c semicolon z right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;f&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mi&gt;c&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;f(z)=z_{2}F_{1}(a,b;c;z)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; for real parameters with &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0 greater-than a less-than-or-equal-to b less-than-or-equal-to c\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mo&gt;≤&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;≤&lt;/mml:mo&gt; &lt;mml:mi&gt;c&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;0&gt;ale ble c&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and its variant &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g left-parenthesis z right-parenthesis equals z 2 upper F 2 left-parenthesis a comma b semicolon c semicolon z squared right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:mi&gt;c&lt;/mml:mi&gt; &lt;mml:mo&gt;;&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;/mml:msup&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;g(z)=z_{2}F_{2}(a,b;c;z^2)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Our first purpose is to solve the range problems for &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;f&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;f&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;g&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;g&lt;/mml:annotation","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Schur-Weyl type duality for twisted weak modules over a vertex algebra","authors":"Kenichiro Tanabe","doi":"10.1090/proc/16843","DOIUrl":"https://doi.org/10.1090/proc/16843","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;V&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; be a vertex algebra of countable dimension, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;G&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; a subgroup of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A u t upper V\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;AutV&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; of finite order, &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V Superscript upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;V^{G}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; the fixed point subalgebra of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;V&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; under the action of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;G&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper S\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"script\"&gt;S&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathscr {S}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; a finite &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;G&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-stable set of inequivalent irreducible twisted weak &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;V&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-modules associated with possibly different automorphisms in &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}