We will now make use of the results from the previous section to extend the analysis of Kac–Moody billiards to include also theories whose U-duality symmetries are described by algebras that are non-split. The key concepts are that of restricted root systems, restricted Weyl group – and the associated concept of maximal split subalgebra – as well as the Iwasawa decomposition already encountered above. These play a prominent role in our discussion as they determine the billiard structure. We mainly follow .
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