量子Loop代数U_(q)(L(sl_(2)))的单权模  

Simple Weight Modules of Quantum Loop Algebra U_(q)(L(sl_(2)))

作　　者：吴青云 谭易兰 夏利猛 WU Qingyun;TAN Yilan;XIA Limeng(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,Jiangsu Province,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013

出　　处：《吉林大学学报（理学版）》2024年第2期256-262,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12171155)。

摘　　要：用构造的方法解决量子Loop代数U_(q)(L(sl_(2)))具有一个一维权空间的单权模的结构问题,得到了任意一个具有一维权空间的单权模必同构于U_(q)(L(sl_(2)))的四类单权模之一.此外,还构造了一类权空间维数为2的既非最高权也非最低权的量子Loop代数U_(q)(L(sl_(2)))的单权模.The structural problem of simple weight modules with a one-dimensional weight space in the quantum Loop algebra U_(q)(L(sl_(2)))was solved by using a construction method,and it was obtained that any simple weight module with a one-dimensional weight space must be isomorphic to one of the four classes of simple weight modules of U_(q)(L(sl_(2))).In addition,a class of simple weight modules of the quantum Loop algebra U_(q)(L(sl_(2)))with weight space dimension of 2,which was neither the highest weight nor the lowest weight,was constructed.

关 键 词：量子Loop代数 权模 单模 Dense模 

分 类 号：O152.5[理学—数学]