楊代數
在表示論中,楊代數(或楊子、Yangian)是一種無限維的霍普夫代數和量子群。這是以楊振寧命名的。俄羅斯物理學家弗拉基米爾·德林費爾德和路德維希·法捷耶夫首先研究了楊子。
定義
若a是半單李代數,Y(a)是無限維的霍普夫代數(跟泛包絡代數有關係)。Y(a)是楊代數。
有些方程
若
若R-矩陣是 R(z)= I+ z-1 P
應用
閱讀
- Chari, Vyjayanthi; Andrew Pressley. A Guide to Quantum Groups. Cambridge, U.K.: Cambridge University Press. 1994. ISBN 0-521-55884-0.
- Drinfeld, Vladimir Gershonovich. Алгебры Хопфа и квантовое уравнение Янга-Бакстера [Hopf algebras and the quantum Yang–Baxter equation]. Doklady Akademii Nauk SSSR. 1985, 283 (5): 1060–1064 (俄語).
- Drinfeld, V. G. A new realization of Yangians and of quantum affine algebras. Doklady Akademii Nauk SSSR. 1987, 296 (1): 13–17 (俄語). 翻譯在 Soviet Mathematics - Doklady. 1988, 36 (2): 212–216. 缺少或
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為空 (幫助) - Drinfeld, V. G. Вырожденные аффинные алгебры Гекке и янгианы [Degenerate affine Hecke algebras and Yangians]. Funktsional'nyi Analiz I Ego Prilozheniya. 1986, 20 (1): 69–70. MR 0831053. Zbl 0599.20049 (俄語). 翻譯在 Drinfeld, V. G. Degenerate affine hecke algebras and Yangians. Functional Analysis and Its Applications. 1986, 20 (1): 58–60. doi:10.1007/BF01077318.
- Molev, Alexander Ivanovich. Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society. 2007. ISBN 978-0-8218-4374-1.
- Bernard, Denis. An Introduction to Yangian Symmetries. NATO ASI Series. 1993, 310 (5): 39–52. ISBN 978-1-4899-1518-4. arXiv:hep-th/9211133
. doi:10.1007/978-1-4899-1516-0_4.
- MacKay, Niall. Introduction to Yangian Symmetry in Integrable Field Theory. International Journal of Modern Physics A. 2005, 20 (30): 7189–7217. Bibcode:2005IJMPA..20.7189M. arXiv:hep-th/0409183
. doi:10.1142/s0217751x05022317.
- Drummond, James; Henn, Johannes; Plefka, Jan. Yangian Symmetry of Scattering Amplitudes in N = 4 super Yang-Mills Theory. Journal of High Energy Physics. 2009, 2009 (5): 046. Bibcode:2009JHEP...05..046D. arXiv:0902.2987
. doi:10.1088/1126-6708/2009/05/046.
參考文獻
- ^ Beisert, N. (2007). The S-matrix of AdS/CFT and Yangian symmetry. arXiv preprint arXiv:0704.0400.
- ^ Spill, F. (2009). Weakly coupled N= 4 Super Yang-Mills and N= 6 Chern-Simons theories from u (2| 2) Yangian symmetry. Journal of High Energy Physics, 2009(03), 014, https://arxiv.org/abs/0810.3897 (頁面存檔備份,存於互聯網檔案館)