{"title":"关于à 2群的边界C *-代数的k理论","authors":"O. King, G. Robertson","doi":"10.1017/IS011005004JKT158","DOIUrl":null,"url":null,"abstract":"Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"521-536"},"PeriodicalIF":0.0000,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011005004JKT158","citationCount":"0","resultStr":"{\"title\":\"On the K-theory of boundary C *-algebras of à 2 groups\",\"authors\":\"O. King, G. Robertson\",\"doi\":\"10.1017/IS011005004JKT158\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"9 1\",\"pages\":\"521-536\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS011005004JKT158\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS011005004JKT158\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS011005004JKT158","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the K-theory of boundary C *-algebras of à 2 groups
Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.
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