{"title":"霍普夫代数","authors":"Owen Sharpe, M. Mastnak, Naoki Sasakura","doi":"10.1142/8055","DOIUrl":null,"url":null,"abstract":"We define a Hopf algebra and give a variety of examples of varying complexity. To facilitate the definition, we first define the commutative diagram, the tensor product, and an algebra/coalgebra/bialgebra. We briefly discuss the duality between algebras and coalgebras. Prior to introducing the non-commutative Hopf algebras of Sweedler and Taft, we define the q-binomial coefficient and prove a related lemma from q-series which allows an explicit formula for the coproduct of a Taft algebra.","PeriodicalId":140374,"journal":{"name":"Graduate Studies in Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"965","resultStr":"{\"title\":\"Hopf algebras\",\"authors\":\"Owen Sharpe, M. Mastnak, Naoki Sasakura\",\"doi\":\"10.1142/8055\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define a Hopf algebra and give a variety of examples of varying complexity. To facilitate the definition, we first define the commutative diagram, the tensor product, and an algebra/coalgebra/bialgebra. We briefly discuss the duality between algebras and coalgebras. Prior to introducing the non-commutative Hopf algebras of Sweedler and Taft, we define the q-binomial coefficient and prove a related lemma from q-series which allows an explicit formula for the coproduct of a Taft algebra.\",\"PeriodicalId\":140374,\"journal\":{\"name\":\"Graduate Studies in Mathematics\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"965\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Graduate Studies in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/8055\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graduate Studies in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/8055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We define a Hopf algebra and give a variety of examples of varying complexity. To facilitate the definition, we first define the commutative diagram, the tensor product, and an algebra/coalgebra/bialgebra. We briefly discuss the duality between algebras and coalgebras. Prior to introducing the non-commutative Hopf algebras of Sweedler and Taft, we define the q-binomial coefficient and prove a related lemma from q-series which allows an explicit formula for the coproduct of a Taft algebra.
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