|
|
|
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 |
|
|
|
|
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.
|
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
|
| [1] |
Baez J and Dolan J 1998 Contemp. Math. 230 1
|
| [2] |
Khovanov M 2001 Comm. Algebra 29 5033
|
| [3] |
Lauda A D 2010 Adv. Math. 225 3327
|
| [4] |
Khovanov M 2010 arXiv: 1009.3295v1 [math.RT]
|
| [5] |
Cautis S and Licata A 2010 arXiv/: 1009.5147v2 [math.QA]
|
| [6] |
Licata A and Savage A 2011 arXiv/: 1101.0420v1 [math.RT]
|
| [7] |
Wang N, Wang Z X, Wu K and Yang Z F 2011 Commun. Theor. Phys. 56 37
|
| [8] |
Chang W J, Wang Z X, Wu K and Yang Z F 2011 Commun. Theor. Phys. 56 207
|
| [9] |
Baez J and Dolan J 2000 arXiv/: math/0004133v1 [math.QA]
|
| [10] |
Morton J 2006 Theory Appl. Categ. 16 785
|
| [11] |
Vicary J 2008 Int. J. Theor. Phys. 47 3408
|
| [12] |
Heunen C, Landsman N P and Spitters B 2009 Comm. Math. Phys. 291 63
|
| [13] |
Abramsky S and Coecke B 2008 arXiv/: 0808.1023v1 [quant-ph]
|
| [14] |
Stirling S D and Wu Y S 2009 arXiv/: 0909.0988v1 [quant-ph]
|
| [15] |
Isham C J 2010 arXiv/: 1004.3564v1 [quant-ph]
|
| [16] |
Chaichian M, Felipe R G and Montonen C 1993 J. Phys. A: Math. Gen. 26 4017
|
| [17] |
Kwek L C and Oh C H 1998 Lett. Math. Phys. 44 273
|
| [18] |
Eremin V V and Meldianov A A 2006 Theor. Math. Phys. 147 709
|
| [19] |
Swamy P N 2006 Int. J. Mod. Phys. B 20 2537
|
| [20] |
Lin B S and Wu K 2012 “A Categorification of the Boson Oscillator” Commun. Theor. Phys. (to appear)
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
