{"title":"The Nonvanishing First Hochschild Cohomology of Twisted Finite Simple Group Algebras","authors":"William Murphy","doi":"10.1007/s10468-022-10195-6","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>G</i> be a finite simple group and <i>k</i> be an algebraically closed field of prime characteristic dividing the order of <i>G</i>. We show that for all 2-cocycles <i>α</i> ∈ <i>Z</i><sup>2</sup>(<i>G</i>;<i>k</i><sup>×</sup>), the first Hochschild cohomology group of the twisted group algebra <i>H</i><i>H</i><sup>1</sup>(<i>k</i><sub><i>α</i></sub><i>G</i>) is nonzero.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-022-10195-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a finite simple group and k be an algebraically closed field of prime characteristic dividing the order of G. We show that for all 2-cocycles α ∈ Z2(G;k×), the first Hochschild cohomology group of the twisted group algebra HH1(kαG) is nonzero.
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