{"title":"A universal property of semigroup \\(C^*\\)-algebras generated by cones in groups of rationals","authors":"Renat Gumerov, Anatoliy Kuklin, Ekaterina Lipacheva","doi":"10.1007/s43034-024-00374-5","DOIUrl":null,"url":null,"abstract":"<div><p>The article deals with the reduced semigroup <span>\\(C^*\\)</span>-algebras for the positive cones in ordered abelian groups. These <span>\\(C^*\\)</span>-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup <span>\\(C^*\\)</span>-algebras as the universal <span>\\(C^*\\)</span>-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup <span>\\(C^*\\)</span>-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal <span>\\(C^*\\)</span>-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-024-00374-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The article deals with the reduced semigroup \(C^*\)-algebras for the positive cones in ordered abelian groups. These \(C^*\)-algebras are generated by the regular isometric representations of the cones. Using the universal property of the isometric representations for the positive cones, we treat the reduced semigroup \(C^*\)-algebras as the universal \(C^*\)-algebras which are defined by sets of generators subject to relations. For arbitrary sequences of prime numbers, we consider the ordered groups of rational numbers determined by these sequences and the reduced semigroup \(C^*\)-algebras of the positive cones in these groups. It is shown that such an algebra can be characterized as a universal \(C^*\)-algebra generated by a countable set of isometries subject to polynomial relations associated with a sequence of prime numbers.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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