{"title":"克莱因曲面基本群的线性表示源自克利福德代数的旋量表示","authors":"Ewa Tyszkowska","doi":"10.1007/s13163-023-00483-0","DOIUrl":null,"url":null,"abstract":"<p>We study actions of multiplicative subgroups of Clifford algebras on Riemann surfaces. We show that every Klein surface of algebraic genus greater than 1 is isomorphic to the orbit space of such an action. We obtain linear representations of fundamental groups of Klein surfaces by using the spinor representations of Clifford algebras.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear representations of fundamental groups of Klein surfaces derived from spinor representations of Clifford algebras\",\"authors\":\"Ewa Tyszkowska\",\"doi\":\"10.1007/s13163-023-00483-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study actions of multiplicative subgroups of Clifford algebras on Riemann surfaces. We show that every Klein surface of algebraic genus greater than 1 is isomorphic to the orbit space of such an action. We obtain linear representations of fundamental groups of Klein surfaces by using the spinor representations of Clifford algebras.</p>\",\"PeriodicalId\":501429,\"journal\":{\"name\":\"Revista Matemática Complutense\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matemática Complutense\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13163-023-00483-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matemática Complutense","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13163-023-00483-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Linear representations of fundamental groups of Klein surfaces derived from spinor representations of Clifford algebras
We study actions of multiplicative subgroups of Clifford algebras on Riemann surfaces. We show that every Klein surface of algebraic genus greater than 1 is isomorphic to the orbit space of such an action. We obtain linear representations of fundamental groups of Klein surfaces by using the spinor representations of Clifford algebras.
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