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 obtai...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）.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 10871135, 11031005, and 10871227
文摘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）.
