{"title":"Averages and the $\\ell ^{q,1}$ cohomology of Heisenberg groups","authors":"P. Pansu, F. Tripaldi","doi":"10.5802/ambp.384","DOIUrl":null,"url":null,"abstract":"Averages are invariants defined on the $\\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\\ell^1$ cohomology vanishes in these cases.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematiques Blaise Pascal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/ambp.384","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 10
Abstract
Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these cases.
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