{"title":"A Matsumoto type theorem for \\(GL_n\\) over rings of non-commutative Laurent polynomials","authors":"Ryusuke Sugawara","doi":"10.1007/s40062-024-00345-6","DOIUrl":null,"url":null,"abstract":"<div><p>We give a Matsumoto-type presentation of <span>\\(K_2\\)</span>-groups over rings of non-commutative Laurent polynomials, which is a non-commutative version of M. Tomie’s result for loop groups. Our main idea is induced by U. Rehmann’s approach in the case of division rings.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","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/s40062-024-00345-6","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
We give a Matsumoto-type presentation of \(K_2\)-groups over rings of non-commutative Laurent polynomials, which is a non-commutative version of M. Tomie’s result for loop groups. Our main idea is induced by U. Rehmann’s approach in the case of division rings.
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