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.
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