A diagrammatic categorification of q-boson and q-fermion algebras |
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| Authors: | Cai Li-Qiang Lin Bing-Sheng and Wu Ke |
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| Institution: | School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;School of Mathematical Sciences, Capital Normal University, Beijing 100048, China |
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| 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. |
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| Keywords: | categorification q-boson algebra q-Fock state q-fermion algebra |
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