{"title":"On the polynomiality conjecture of cluster realization of quantum groups","authors":"","doi":"10.1016/j.jalgebra.2024.08.031","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002186932400499X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.
期刊介绍:
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.