{"title":"Hopf共括号,编织方程和交叉","authors":"HUIHUI ZHENG, FANGSHU LI, TIANSHUI MA","doi":"10.59277/mrar.2023.25.75.3.481","DOIUrl":null,"url":null,"abstract":"In this paper, we mainly give some equivalent characterisations of Hopf cobraces, show that the full subcategory HCB(A) of Hopf co-braces is equivalent to the full subcategory C(A) of bijective 1-cocycles, and prove that the full subcategory HCB(A) is also equivalent to the category M(A) of Hopf matched pairs. Moreover, we construct many Hopf co-braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel’d doubles of finite dimensional Hopf algebras. And we also give a sufficient and necessary condition for a given bicrossed coproduct A ▷◁ H to be a Hopf co-brace if A or H is a Hopf co-brace","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"26 1","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"HOPF CO-BRACE, BRAID EQUATION AND BICROSSED\",\"authors\":\"HUIHUI ZHENG, FANGSHU LI, TIANSHUI MA\",\"doi\":\"10.59277/mrar.2023.25.75.3.481\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we mainly give some equivalent characterisations of Hopf cobraces, show that the full subcategory HCB(A) of Hopf co-braces is equivalent to the full subcategory C(A) of bijective 1-cocycles, and prove that the full subcategory HCB(A) is also equivalent to the category M(A) of Hopf matched pairs. Moreover, we construct many Hopf co-braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel’d doubles of finite dimensional Hopf algebras. And we also give a sufficient and necessary condition for a given bicrossed coproduct A ▷◁ H to be a Hopf co-brace if A or H is a Hopf co-brace\",\"PeriodicalId\":49858,\"journal\":{\"name\":\"Mathematical Reports\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Reports\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.59277/mrar.2023.25.75.3.481\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59277/mrar.2023.25.75.3.481","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we mainly give some equivalent characterisations of Hopf cobraces, show that the full subcategory HCB(A) of Hopf co-braces is equivalent to the full subcategory C(A) of bijective 1-cocycles, and prove that the full subcategory HCB(A) is also equivalent to the category M(A) of Hopf matched pairs. Moreover, we construct many Hopf co-braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel’d doubles of finite dimensional Hopf algebras. And we also give a sufficient and necessary condition for a given bicrossed coproduct A ▷◁ H to be a Hopf co-brace if A or H is a Hopf co-brace
期刊介绍:
The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500.
Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.