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

doi:10.1088/1674-1056/21/2/020201

中国物理B ›› 2012, Vol. 21 ›› Issue (2): 20201-020201.doi: 10.1088/1674-1056/21/2/020201

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蔡立强,林冰生,吴可

收稿日期:2011-09-13 修回日期:2011-09-22 出版日期:2012-01-30 发布日期:2012-01-30
通讯作者: 林冰生,gdjylbs@mail.ustc.edu.cn E-mail:gdjylbs@mail.ustc.edu.cn

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

Cai Li-Qiang(蔡立强), Lin Bing-Sheng(林冰生)^†, and Wu Ke(吴可)

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2011-09-13 Revised:2011-09-22 Online:2012-01-30 Published:2012-01-30
Contact: Lin Bing-Sheng,gdjylbs@mail.ustc.edu.cn E-mail:gdjylbs@mail.ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10975102, 10871135, 11031005, and 11075014).

摘要/Abstract

Abstract: 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.

Key words: categorification, q-boson algebra, q-Fock state, q-fermion algebra

中图分类号: (Rings and algebras)

02.10.Hh

03.65.Ca (Formalism) 03.65.Fd (Algebraic methods)

蔡立强,林冰生,吴可. [J]. 中国物理B, 2012, 21(2): 20201-020201.

Cai Li-Qiang(蔡立强), Lin Bing-Sheng(林冰生), and Wu Ke(吴可) . A diagrammatic categorification of q-boson and q-fermion algebras[J]. Chin. Phys. B, 2012, 21(2): 20201-020201.

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

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