翻译霍普夫代数和霍普夫堆

Pub Date : 2024-08-21 DOI:10.1007/s10468-024-10283-9

Tomasz Brzeziński, Małgorzata Hryniewicka

{"title":"翻译霍普夫代数和霍普夫堆","authors":"Tomasz Brzeziński, Małgorzata Hryniewicka","doi":"10.1007/s10468-024-10283-9","DOIUrl":null,"url":null,"abstract":"<div><p>To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of a Hopf heap with the translation Hopf algebra isomorphic to the acting Hopf algebra. It is then shown that this assignment establishes an equivalence between categories of Hopf heaps and Hopf-Galois co-objects.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10283-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Translation Hopf Algebras and Hopf Heaps\",\"authors\":\"Tomasz Brzeziński, Małgorzata Hryniewicka\",\"doi\":\"10.1007/s10468-024-10283-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of a Hopf heap with the translation Hopf algebra isomorphic to the acting Hopf algebra. It is then shown that this assignment establishes an equivalence between categories of Hopf heaps and Hopf-Galois co-objects.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10468-024-10283-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-024-10283-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10283-9","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

格伦斯潘的每个霍普夫堆或量子同调器都与一个平移霍普夫代数相关联。这个平移霍普夫代数作用于霍普夫堆，使其成为霍普夫-伽罗瓦共客体。反过来，任何 Hopf-Galois 同对象都具有 Hopf 堆的自然结构，其平移 Hopf 代数与作用的 Hopf 代数同构。然后证明，这一赋值在霍普夫堆和霍普夫-伽罗瓦共客体范畴之间建立了等价关系。

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

Translation Hopf Algebras and Hopf Heaps

To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of a Hopf heap with the translation Hopf algebra isomorphic to the acting Hopf algebra. It is then shown that this assignment establishes an equivalence between categories of Hopf heaps and Hopf-Galois co-objects.

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