Coxeter-Dynkin diagram
English
![](Images/wiktionary/Finite_coxeter.svg.png.webp)
Some Coxeter-Dynkin diagrams
Etymology
After mathematicians H. S. M. Coxeter and Eugene Dynkin.
Noun
Coxeter-Dynkin diagram (plural Coxeter-Dynkin diagrams)
- (geometry, algebra) A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
- A Coxeter-Dynkin diagram encodes the information in a Coxeter matrix, which in turn encodes the presentation of a Coxeter group.
- 1995 June, R. V. Moody, J. Patera, Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices, Canadian Journal of Mathematics, page 597,
- Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.
- 2000, Andrei Gabrielov, Coxeter-Dynkin diagrams and singularities, Evgeniĭ Borisovich Dynkin, A. A. Yushkevich, Gary M. Seitz, A. L. Onishchik (editors), Selected Papers of E. B. Dynkin with Commentary, page 367,
- There is a deep and only partially understood connection between the classification and structure of singularities and the Coxeter-Dynkin diagrams introduced by H. S .M. Coxeter for classification of reflection-generated groups and by E. B. Dynkin for classification of semisimple Lie algebras.
- 2012, Igor V. Dolgachev, Classical Algebraic Geometry: A Modern View, page 363:
- For 3 ≤ n ≤ 5, we will use En to denote the Coxeter-Dynkin diagrams of types A1 + A2(N = 3), A4(N = 4) and D5(N = 5).
Synonyms
- (graph with numerically labelled edges): Coxeter diagram, Coxeter graph
See also
- Dynkin diagram