{"title":"Coalgebra‐Galois Extensions from the Extension Theory Point of View","authors":"T. Brzeziński","doi":"10.1201/9780429187919-4","DOIUrl":"https://doi.org/10.1201/9780429187919-4","url":null,"abstract":"Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"116 2-3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132462645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic Versions of a Finite‐Dimensional Quantum Groupoid","authors":"D. Nikshych, L. Vainerman","doi":"10.1201/9780429187919-10","DOIUrl":"https://doi.org/10.1201/9780429187919-10","url":null,"abstract":"We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak $C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf bimodule, the notion introduced by J.-M. Vallin. We also study the structure and construct examples of finite dimensional quantum groupoids.","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133012797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasi‐Hopf Algebras and the Centre of a Tensor Category","authors":"F. Panaite, F. Oystaeyen","doi":"10.1201/9780429187919-11","DOIUrl":"https://doi.org/10.1201/9780429187919-11","url":null,"abstract":"","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125043812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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