The Dynkin diagram is a graphic means of describing abstract root systems or, equivalently, of characterizing Cartan matrices. The command DynkinDiagram plots the Dynkin diagram for each root type $A_m$, $B_m$, $C_m$, ${\mathrm{D}}_m$, $E_6$, $E_7$, $E_8$, $F_4$, $G_2$.

$$See Details of Cartan Matrices and Dynkin Diagrams for more information on the relationship between these two ways of characterizing complex simple Lie algebras.

For real Lie algebras, the Satake diagrams provide the counterpart to the Dynkin diagrams.

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{LieAlgebras}\right)\:$

$\mathrm{DynkinDiagram}\left(''A''\,6\right)$

$\mathrm{DynkinDiagram}\left(''B''\,6\right)$

$\mathrm{DynkinDiagram}\left(''C''\,6\right)$

$\mathrm{DynkinDiagram}\left(''D''\,6\right)$

$\mathrm{DynkinDiagram}\left(''F''\,4\right)$

$\mathrm{DynkinDiagram}\left(''G''\,2\right)$

$\mathrm{DynkinDiagram}\left(''E''\,8\right)$

$\mathrm{DynkinDiagram}\left(''E''\,8\,\mathrm{version}=2\right)$