Figure 24: The Dynkin diagram of the hyperbolic Kac–Moody algebra which controls the
billiard dynamics of pure gravity in dimensions. The nodes represent
the “symmetry walls” arising from the off-diagonal components of the spatial metric, and the node
corresponds to a “curvature wall” coming from the spatial curvature. The horizontal line is the
Dynkin diagram of the underlying -subalgebra and the two topmost nodes, and ,
give the affine- and overextension, respectively.
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