ディンキン図形
出典: フリー百科事典『ウィキペディア(Wikipedia)』 (2021/04/17 01:16 UTC 版)
関連項目
- 佐武図形
- ウィキブックス Klassifikation von Wurzelsystemen (ルート系の分類) (ドイツ語)
参考文献
- Dynkin, E. B. (1947), “The structure of semi-simple algebras .” (ロシア語), Uspehi Matem. Nauk, (N.S.) 2 (4(20)): 59–127
- Bourbaki, Nicolas (1968), “Chapters 4–6”, Groupes et algebres de Lie, Paris: Hermann
- Jacobson, Nathan (1971-06-01), Exceptional Lie Algebras (1 ed.), CRC Press, ISBN 0-8247-1326-5
- Humphreys, James E. (1972), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7
- Fulton, William; Harris, Joe (1991), Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics, 129, New York: Springer-Verlag, ISBN 978-0-387-97495-8, MR1153249, ISBN 978-0-387-97527-6
- Dynkin, Evgeniĭ Borisovich; Alexander Adolph Yushkevich; Gary M. Seitz; A. L. Onishchik (2000), Selected papers of E.B. Dynkin with commentary, AMS Bookstore, ISBN 978-0-8218-1065-1
- Knapp, Anthony W. (2002), Lie groups beyond an introduction (2nd ed.), Birkhäuser, ISBN 978-0-8176-4259-4
- Stekolshchik, R. (2008), Notes on Coxeter Transformations and the McKay Correspondence, Springer Monographs in Mathematics, doi:10.1007/978-3-540-77398-3, ISBN 978-3-540-77398-6
外部リンク
- Dynkin diagram at Encyclopaedia of Mathematics
- John Baez on the ubiquity of Dynkin diagrams in mathematics
- Web tool for making publication-quality Dynkin diagrams with labels (written in JavaScript)
注
出典
- ^ Baez, John (April 13, 1998), This Week's Finds in Mathematical Physics (Week 119)
- ^ Fulton & Harris 1991, Proposition D.40.
- ^ a b c Outer automorphisms of simple Lie Algebras
- ^ & Humphreys 1972, Section 16.5.
- ^ Jacobson 1971, section 7.
- ^ Algebraic geometry and number theory: in honor of Vladimir Drinfeld's 50th Birthday, edited by Victor Ginzburg, p. 47, section 3.6: Cluster folding
- ^ a b Folding by Automorphisms, John Stembridge, 4pp., 79K, 20 August 2008, Other Articles by John Stembridge
- ^ これらの foldings の絵と文献については次を参照:(Stekolshchik 2008, p. 102, remark 5.4).
- ^ Zuber, Jean-Bernard. Generalized Dynkin diagrams and root systems and their folding. pp. 28–30.
- ^ a b Transformations of Dynkin Diagrams, John Armstrong, March 5, 2010
- ^ a b (Knapp 2002, p. 758)
- ^ a b c Why are the Dynkin diagrams E6, E7 and E8 always drawn the way they are drawn?
- ^ Notes on Coxeter Transformations and the McKay correspondence, Rafael Stekolshchik, 2005, Section 2.1 The Cartan matrix and its Tits form p. 27. [1]
- ^ 例えば次を参照: Reflection groups and Coxeter groups, by James E. Humphreys, p. 96
- ^ [2] Infinite dimensional Lie algebras, Victor Kac
- ^ Carbone, L, Chung, S, Cobbs, C, McRae, R, Nandi, D, Naqvi, Y, and Penta, D: Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits, J. Phys. A: Math. Theor. 43 155209, 2010, arXiv:1003.0564
- ^ The symmetry of M-theories, Francois Englert, Laurent Houart, Anne Taormina and Peter West, 2003
- ディンキン図形のページへのリンク