{"title":"Applications of the Freezing Operators on Cluster Algebras","authors":"Fan Qin","doi":"10.1142/S0219498825503578","DOIUrl":null,"url":null,"abstract":"We apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. They also send bases to bases in many cases. In addition, the bases constructed via freezing coincide with those constructed via localization.","PeriodicalId":508127,"journal":{"name":"Journal of Algebra and Its Applications","volume":" 37","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0219498825503578","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 apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. They also send bases to bases in many cases. In addition, the bases constructed via freezing coincide with those constructed via localization.
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