Homological stability for Iwahori–Hecke algebras

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2022-10-08 DOI:10.1112/topo.12262

Richard Hepworth

{"title":"Homological stability for Iwahori–Hecke algebras","authors":"Richard Hepworth","doi":"10.1112/topo.12262","DOIUrl":null,"url":null,"abstract":"<p>We show that the Iwahori–Hecke algebras <math>\n <semantics>\n <msub>\n <mi>H</mi>\n <mi>n</mi>\n </msub>\n <annotation>$\\mathcal {H}_n$</annotation>\n </semantics></math> of type <math>\n <semantics>\n <msub>\n <mi>A</mi>\n <mrow>\n <mi>n</mi>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <annotation>$A_{n-1}$</annotation>\n </semantics></math> satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 4","pages":"2174-2215"},"PeriodicalIF":0.8000,"publicationDate":"2022-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12262","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12262","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: 13

Abstract

We show that the Iwahori–Hecke algebras $H_{n}$ of type $A_{n - 1}$ satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Iwahori-Hecke代数的同调稳定性

证明了类型为A n−1 A_{n-1}$的Iwahori-Hecke代数H n$ \mathcal {H}_n$满足同调稳定性，其中同源性被解释为一个适当的Tor群。我们的结果精确地恢复了在定义参数等于1的情况下对称群的Nakaoka的同调稳定性结果。我们相信这篇论文，以及我们与Boyd在Temperley-Lieb代数上的合作工作，是第一次将同调稳定性技术应用到非群代数上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.