{"title":"Further topics on algebras","authors":"","doi":"10.1090/gsm/193/02","DOIUrl":"https://doi.org/10.1090/gsm/193/02","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"67 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":"127758451","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 language of categories and\u0000 functors","authors":"","doi":"10.1090/gsm/193/13","DOIUrl":"https://doi.org/10.1090/gsm/193/13","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"341 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":"133830007","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 studies the representations of semisimple Lie algebras, with care given to the case of sln(C). We develop and utilize various tools, including the adjoint representation, the Killing form, root space decomposition, and the Weyl group to classify the irreducible representations of semisimple Lie algebras.
{"title":"Representations of semisimple Lie\u0000 algebras","authors":"Abhinav Shrestha","doi":"10.1090/gsm/193/08","DOIUrl":"https://doi.org/10.1090/gsm/193/08","url":null,"abstract":"This paper studies the representations of semisimple Lie algebras, with care given to the case of sln(C). We develop and utilize various tools, including the adjoint representation, the Killing form, root space decomposition, and the Weyl group to classify the irreducible representations of semisimple Lie algebras.","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"5 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131957703","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":"Semisimple Lie algebras","authors":"D. Byrne","doi":"10.1090/gsm/193/06","DOIUrl":"https://doi.org/10.1090/gsm/193/06","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"43 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":"130189771","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: 10.1007/978-1-4684-9443-3_2
J. Humphreys
{"title":"Affine algebraic groups","authors":"J. Humphreys","doi":"10.1007/978-1-4684-9443-3_2","DOIUrl":"https://doi.org/10.1007/978-1-4684-9443-3_2","url":null,"abstract":"","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"20 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":"127775778","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}
In this paper, we explore applications, examples, and representative theo-ries of Symmetric groups in a symmetric group. All elements are all bijections to the set itself, and the group operation is function composition. We begin by discussing the definition of symmetry with a few basic examples and applications. We then introduce and define some real-world applications followed by properties and special elements of symmetric groups. Lastly, we show the subgroup structure of symmetric groups and some of the representative theories.
{"title":"Symmetric groups","authors":"Evelyn Zhu","doi":"10.1090/gsm/193/04","DOIUrl":"https://doi.org/10.1090/gsm/193/04","url":null,"abstract":"In this paper, we explore applications, examples, and representative theo-ries of Symmetric groups in a symmetric group. All elements are all bijections to the set itself, and the group operation is function composition. We begin by discussing the definition of symmetry with a few basic examples and applications. We then introduce and define some real-world applications followed by properties and special elements of symmetric groups. Lastly, we show the subgroup structure of symmetric groups and some of the representative theories.","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"24 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":"121632820","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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