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量子仿射代数Uq（sln）的范畴化
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O413[理学—理论物理;理学—物理]
  • 作者机构：[1]首都师范大学数学科学学院北京100048
  • 相关基金：国家自然科学基金（10975102,11031005,10871135,10871227）和北京市创新团队项目（201007107）资助
作者： 任磊[1], 常文静[1], 王娜[1], 王志玺[1], 吴可[1], 杨紫峰[1]
关键词： 量子仿射代数, 范畴化, 2-表示, Quantum affine algebra, Categorification, 2-representation.
中文摘要：

摘要：用弦图构造了与Lusztig的量子群U=Uq（sln）对应的2一范畴甜和功．其中功是u的Karoubi包络．通过构造功的2-表示，可以证明功的Grothendieck环Ko（u）同构于代数AO，其中U是U的幂等变形，而AD是T3的整形式．由此得到的范畴功就是量子仿射代数Uq（sln）的范畴化．

英文摘要：

We construct 2-categories uand U using string diagrams corresponding to Lusztig＇s quantum group U = Uq（sln）. Here U is the Karoubi envelope of u. By constructing the 2- representation of Lt, we also prove that the Grothendieck ring K0（U） ofU is isomorphic to the algebra U, where U is the idempotented modification of U and U is the integral form of l）. We obtain that the category U could be considered as the categorification of quantum affine algebra Uq（sln）.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
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  • 被引量:5382