Geodesic
Maximum-rank root subsystems of hyperbolic root systems
Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 121-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Kac–Moody algebra is said to be hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. Root subsystems of root systems of algebras of this kind are studied. The main result of the paper is the classification of the maximum-rank regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras. 
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P. V. Tumarkin. Maximum-rank root subsystems of hyperbolic root systems. Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 121-134. http://geodesic.mathdoc.fr/item/SM_2004_195_1_a6/

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