{"title":"论有原理系数的非环量子簇代数","authors":"Junyuan Huang, Xueqing Chen, Ming Ding, Fan Xu","doi":"arxiv-2407.17685","DOIUrl":null,"url":null,"abstract":"In this paper, we focus on a new lower bound quantum cluster algebra which is\ngenerated by the initial quantum cluster variables and the quantum projective\ncluster variables of an acyclic quantum cluster algebra with principle\ncoefficients. We show that the new lower bound quantum cluster algebra\ncoincides with the corresponding acyclic quantum cluster algebra. Moreover, we\nestablish a class of formulas between these generators, and obtain the dual PBW\nbasis of this algebra.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the acyclic quantum cluster algebras with principle coefficients\",\"authors\":\"Junyuan Huang, Xueqing Chen, Ming Ding, Fan Xu\",\"doi\":\"arxiv-2407.17685\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we focus on a new lower bound quantum cluster algebra which is\\ngenerated by the initial quantum cluster variables and the quantum projective\\ncluster variables of an acyclic quantum cluster algebra with principle\\ncoefficients. We show that the new lower bound quantum cluster algebra\\ncoincides with the corresponding acyclic quantum cluster algebra. Moreover, we\\nestablish a class of formulas between these generators, and obtain the dual PBW\\nbasis of this algebra.\",\"PeriodicalId\":501317,\"journal\":{\"name\":\"arXiv - MATH - Quantum Algebra\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Quantum Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.17685\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.17685","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the acyclic quantum cluster algebras with principle coefficients
In this paper, we focus on a new lower bound quantum cluster algebra which is
generated by the initial quantum cluster variables and the quantum projective
cluster variables of an acyclic quantum cluster algebra with principle
coefficients. We show that the new lower bound quantum cluster algebra
coincides with the corresponding acyclic quantum cluster algebra. Moreover, we
establish a class of formulas between these generators, and obtain the dual PBW
basis of this algebra.