Editing Dynkin diagram (section)

=== Example: A<sub>2</sub> ===
[[File:Root system A2.svg|class=skin-invert-image|thumb|The <math>A_2</math> root system]]

For example, the symbol <math>A_2</math> may refer to:
* The '''Dynkin diagram''' with 2 connected nodes, <span class=skin-invert>{{Dynkin|node|3|node}}</span>, which may also be interpreted as a '''[[Coxeter diagram]]'''.
* The '''[[root system]]''' with 2 simple roots at a <math>2\pi/3</math> (120 degree) angle.
* The '''Lie algebra''' <math>\mathfrak{sl}_{2+1} = \mathfrak{sl}_3</math> of [[rank (Lie algebra)|rank]] 2.
* The '''[[Weyl group]]''' of symmetries of the roots (reflections in the hyperplane orthogonal to the roots), isomorphic to the [[symmetric group]] <math>S_3</math> (of order 6).
* The abstract '''[[Coxeter group]]''', presented by generators and relations, <math>\left\langle r_1,r_2 \mid (r_1)^2=(r_2)^2=(r_ir_j)^3=1\right\rangle.</math>