A Categorification of Quantum sl_2  

作　　者：王娜 王志玺 吴可 杨紫峰 

机构地区：[1]School of Mathematical Science,Capital Normal University

出　　处：《Communications in Theoretical Physics》2011年第7期37-45,共9页理论物理通讯（英文版）

基　　金：Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 10871135, 11031005, and 10871227

摘　　要：In this paper, we categorify the algebra Uq（sl2） with the same approach as in [A. Lauda, Adv. Math. （2010）, arXiv：math.QA/0803.3662; M. Khovanov, Comm. Algebra 11 （2001） 5033]. The algebra U =Uq（sl2） is obtained from Uq（sl2） by adjoining a collection of orthogonal idempotents 1λ,λ ∈ P, in which P is the weight lattice of Uq（sl2）. Under such construction the algebra U is decomposed into a direct sum λ∈p 1λ,U1λ. We set the collection of λ∈ P as the objects of the category U, 1-morphisms from λ to λ′ are given by 1λ,U1λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category u from the algebra Uq（sl2）.

关 键 词：quantum affine algebra CATEGORIFICATION 

分 类 号：O413[理学—理论物理]