A diagrammatic categorification of q-boson and q-fermion algebras  

作　　者：Cai Li-qiang Lin Bing-Sheng Wu Ke 蔡立强;林冰生;吴可(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Chinese Physics B》2012年第2期1-8,共8页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.10975102,10871135,11031005,and 11075014)

摘　　要：In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.

关 键 词：CATEGORIFICATION q-boson algebra q-Fock state q-fermion algebra 

分 类 号：O411[理学—理论物理]