An affine Dynkin diagram is a Dynkin diagram associated with an affine Kac-Moody algebra. An untwisted
affine Dynkin diagram can be obtained from a finite Dynkin
diagram by adjoining a vertex corresponding to
the negative of the highest root, with edges determined
by the resulting generalized Cartan matrix. The
classification of affine Kac-Moody algebras
also includes twisted types, to which this highest-root recipe does not in general
apply. Twisted types arise from nontrivial symmetries of finite Dynkin
diagrams, of order 2 or 3, used to twist the construction of the affine Kac-Moody
algebra (Kac 1990). The superscript in 
records this order: 
denotes an untwisted type, whereas 
and 
are examples of twisted types.
Affine Dynkin Diagram
See also
Cartan Matrix, Dynkin Diagram, Root SystemExplore with Wolfram|Alpha
References
Kac, V. G. Infinite-Dimensional Lie Algebras, 3rd ed. Cambridge, England: Cambridge University Press, 1990.Cite this as:
Weisstein, Eric W. "Affine Dynkin Diagram." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AffineDynkinDiagram.html