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

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

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.

Keywords: categorification q-boson algebra q-Fock state q-fermion algebra

Received: 13 September 2011
Revised: 22 September 2011
Accepted manuscript online:

PACS:	02.10.Hh	(Rings and algebras)
	03.65.Ca	(Formalism)
	03.65.Fd	(Algebraic methods)

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

Corresponding Authors: Lin Bing-Sheng,gdjylbs@mail.ustc.edu.cn
E-mail: gdjylbs@mail.ustc.edu.cn

Cite this article:

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 2012 Chin. Phys. B 21 020201

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

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