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

作者机构：School of Mathematical SciencesCapital Normal UniversityBeijing 100048China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2012年第21卷第2期

页      面：1-8页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

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

主　　题：categorification q-boson algebra q-Fock state q-fermion algebra 

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.