{"title":"Coalgebras, bialgebras, and Hopf\u0000 algebras","authors":"","doi":"10.1090/gsm/193/09","DOIUrl":"https://doi.org/10.1090/gsm/193/09","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124013513","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}
Pub Date : 2018-09-24DOI: 10.1007/978-3-0348-8205-7_11
K. Brown, K. Goodearl
{"title":"The Diamond Lemma","authors":"K. Brown, K. Goodearl","doi":"10.1007/978-3-0348-8205-7_11","DOIUrl":"https://doi.org/10.1007/978-3-0348-8205-7_11","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116488191","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}
Pub Date : 2018-09-24DOI: 10.1007/978-3-8348-8159-5_2
G. Harder
{"title":"Some commutative algebra","authors":"G. Harder","doi":"10.1007/978-3-8348-8159-5_2","DOIUrl":"https://doi.org/10.1007/978-3-8348-8159-5_2","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131693719","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}
This paper mainly discussed various characterizations for the finite-dimensional Hopf algebras over algebraically closed field and has characteristic 0. And further showed that the order of antipode of the Hopf algebras is finite, but also provides a hint on how to estimate the order of the antipodes.
{"title":"Finite-dimensional Hopf algebras","authors":"Yuqiu Wei, Beishang Ren","doi":"10.1090/gsm/193/12","DOIUrl":"https://doi.org/10.1090/gsm/193/12","url":null,"abstract":"This paper mainly discussed various characterizations for the finite-dimensional Hopf algebras over algebraically closed field and has characteristic 0. And further showed that the order of antipode of the Hopf algebras is finite, but also provides a hint on how to estimate the order of the antipodes.","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125497901","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":"Background from linear algebra","authors":"","doi":"10.1090/gsm/193/14","DOIUrl":"https://doi.org/10.1090/gsm/193/14","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132591432","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":"Groups and group algebras","authors":"","doi":"10.1090/gsm/193/03","DOIUrl":"https://doi.org/10.1090/gsm/193/03","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131909925","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}
Pub Date : 2018-09-24DOI: 10.1007/3-540-27427-8_18
J. Dusel
{"title":"Root systems","authors":"J. Dusel","doi":"10.1007/3-540-27427-8_18","DOIUrl":"https://doi.org/10.1007/3-540-27427-8_18","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"52 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133003728","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":"Representations and actions","authors":"","doi":"10.1090/gsm/193/10","DOIUrl":"https://doi.org/10.1090/gsm/193/10","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115067267","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":"Lie algebras and enveloping algebras","authors":"","doi":"10.1090/gsm/193/05","DOIUrl":"https://doi.org/10.1090/gsm/193/05","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122421450","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":"The symmetric ring of quotients","authors":"","doi":"10.1090/gsm/193/17","DOIUrl":"https://doi.org/10.1090/gsm/193/17","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133610156","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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