特征二中的非etherian GL 矩阵

arXiv - MATH - Representation Theory Pub Date : 2024-08-08 DOI:arxiv-2408.04630

Karthik Ganapathy

{"title":"特征二中的非etherian GL 矩阵","authors":"Karthik Ganapathy","doi":"arxiv-2408.04630","DOIUrl":null,"url":null,"abstract":"Over fields of characteristic two, we construct an infinite ascending chain\nof GL-stable ideals in the coordinate ring of infinite (skew-)symmetric\nmatrices. This construction provides the first known example of a\nnon-noetherian GL-algebra, thereby resolving a long-standing open question in\nthe area. Our results build on the work of Draisma, Krasilnikov, and Krone.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"77 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-noetherian GL-algebras in characteristic two\",\"authors\":\"Karthik Ganapathy\",\"doi\":\"arxiv-2408.04630\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Over fields of characteristic two, we construct an infinite ascending chain\\nof GL-stable ideals in the coordinate ring of infinite (skew-)symmetric\\nmatrices. This construction provides the first known example of a\\nnon-noetherian GL-algebra, thereby resolving a long-standing open question in\\nthe area. Our results build on the work of Draisma, Krasilnikov, and Krone.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"77 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.04630\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.04630","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在特征二域上，我们在无限（偏斜）对称矩阵的坐标环中构造了一个无限上升的 GL 稳定理想链。这一构造提供了第一个已知的无醚 GL 代数的例子，从而解决了该领域一个长期悬而未决的问题。我们的结果建立在 Draisma、Krasilnikov 和 Krone 的研究基础之上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Non-noetherian GL-algebras in characteristic two

Over fields of characteristic two, we construct an infinite ascending chain of GL-stable ideals in the coordinate ring of infinite (skew-)symmetric matrices. This construction provides the first known example of a non-noetherian GL-algebra, thereby resolving a long-standing open question in the area. Our results build on the work of Draisma, Krasilnikov, and Krone.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Representation Theory

自引率

0.00%

发文量