{"title":"有限亚当斯霍普夫自治体的稳定皮卡德群及其在 R-motivic Steenrod 子代数中的应用 <mml:math xns:mmml=\"http://www.w3.org/1998/Math/MathML\"","authors":"Xu Gao , Ang Li","doi":"10.1016/j.jpaa.2024.107732","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the rigidity of the stable comodule category of a specific class of Hopf algebroids known as <em>finite Adams</em>, shedding light on its Picard group. Then, we establish a reduction process through base changes, enabling us to effectively compute the Picard group of the <figure><img></figure><em>-motivic mod</em> 2 <em>Steenrod subalgebra</em> <figure><img></figure>. Our computation shows that <figure><img></figure> is isomorphic to <figure><img></figure>, where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the <figure><img></figure><em>-motivic joker J</em>.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"228 11","pages":"Article 107732"},"PeriodicalIF":0.7000,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The stable Picard group of finite Adams Hopf algebroids with an application to the R-motivic Steenrod subalgebra AR(1)\",\"authors\":\"Xu Gao , Ang Li\",\"doi\":\"10.1016/j.jpaa.2024.107732\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate the rigidity of the stable comodule category of a specific class of Hopf algebroids known as <em>finite Adams</em>, shedding light on its Picard group. Then, we establish a reduction process through base changes, enabling us to effectively compute the Picard group of the <figure><img></figure><em>-motivic mod</em> 2 <em>Steenrod subalgebra</em> <figure><img></figure>. Our computation shows that <figure><img></figure> is isomorphic to <figure><img></figure>, where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the <figure><img></figure><em>-motivic joker J</em>.</p></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"228 11\",\"pages\":\"Article 107732\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924001294\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001294","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们研究了一类被称为有限亚当斯的特定霍普夫等价体的稳定逗点范畴的刚性,揭示了它的皮卡群。然后,我们建立了一个通过基变化的还原过程,使我们能够有效地计算-motivic mod 2 Steenrod 子代数的皮卡群。我们的计算表明,它与 ,同构,其中两个等级来自动机分级,一个来自代数环函子,最后一个由 -动机小丑 J 生成。
The stable Picard group of finite Adams Hopf algebroids with an application to the R-motivic Steenrod subalgebra AR(1)
In this paper, we investigate the rigidity of the stable comodule category of a specific class of Hopf algebroids known as finite Adams, shedding light on its Picard group. Then, we establish a reduction process through base changes, enabling us to effectively compute the Picard group of the -motivic mod 2 Steenrod subalgebra . Our computation shows that is isomorphic to , where two ranks come from the motivic grading, one from the algebraic loop functor, and the last is generated by the -motivic joker J.
期刊介绍:
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.