{"title":"分次C*-代数,分次k -理论,和扭曲p图C*-代数","authors":"A. Kumjian, D. Pask, A. Sims","doi":"10.7900/JOT.2017SEP28.2192","DOIUrl":null,"url":null,"abstract":"We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K-theory of a graph C*-algebra carrying such a grading.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras\",\"authors\":\"A. Kumjian, D. Pask, A. Sims\",\"doi\":\"10.7900/JOT.2017SEP28.2192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K-theory of a graph C*-algebra carrying such a grading.\",\"PeriodicalId\":351745,\"journal\":{\"name\":\"arXiv: Operator Algebras\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7900/JOT.2017SEP28.2192\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7900/JOT.2017SEP28.2192","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras
We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K-theory of a graph C*-algebra carrying such a grading.