具有对合的紧李群的等变k理论

arXiv: K-Theory and Homology Pub Date : 2014-01-30 DOI:10.1017/IS014002004JKT254

P. Hu, I. Kríz, P. Somberg

{"title":"具有对合的紧李群的等变k理论","authors":"P. Hu, I. Kríz, P. Somberg","doi":"10.1017/IS014002004JKT254","DOIUrl":null,"url":null,"abstract":"For a compact simply connected simple Lie group $G$ with an involution $\\alpha$, we compute the $G\\rtimes \\Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\\Z/2$ acts either by $\\alpha$ or by $g\\mapsto \\alpha(g)^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equivariant K-theory of compact Lie groups with involution\",\"authors\":\"P. Hu, I. Kríz, P. Somberg\",\"doi\":\"10.1017/IS014002004JKT254\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a compact simply connected simple Lie group $G$ with an involution $\\\\alpha$, we compute the $G\\\\rtimes \\\\Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\\\\Z/2$ acts either by $\\\\alpha$ or by $g\\\\mapsto \\\\alpha(g)^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS014002004JKT254\",\"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: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS014002004JKT254","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于具有对合函数的紧单连通单李群$G$，我们计算了$G$的$G\rt乘以$ Z/2$-等变k理论，其中$G$是共轭作用的，$ Z/2$是共轭作用的，$ Z/2$是共轭作用的，$ Z/2$是共轭作用的，$G\ mapsto \alpha(G)^{-1}$。我们也给出了这些群以及$K_G(G)$的表示理论解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Equivariant K-theory of compact Lie groups with involution

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: K-Theory and Homology

自引率

0.00%

发文量

期刊最新文献

Homology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spaces An identification of the Baum-Connes and Davis-L\"uck assembly maps Algebraic K-theory of quasi-smooth blow-ups and cdh descent Note on linear relations in Galois cohomology and étale K-theory of curves Weibel’s conjecture for twisted K-theory