Geodesic
Maximum-rank root subsystems of hyperbolic root systems
Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 121-134 
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/
@article{SM_2004_195_1_a6,
     author = {P. V. Tumarkin},
     title = {Maximum-rank root subsystems of hyperbolic root systems},
     journal = {Sbornik. Mathematics},
     pages = {121--134},
     year = {2004},
     volume = {195},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_1_a6/}
}
TY  - JOUR
AU  - P. V. Tumarkin
TI  - Maximum-rank root subsystems of hyperbolic root systems
JO  - Sbornik. Mathematics
PY  - 2004
SP  - 121
EP  - 134
VL  - 195
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_2004_195_1_a6/
LA  - en
ID  - SM_2004_195_1_a6
ER  - 
%0 Journal Article
%A P. V. Tumarkin
%T Maximum-rank root subsystems of hyperbolic root systems
%J Sbornik. Mathematics
%D 2004
%P 121-134
%V 195
%N 1
%U http://geodesic.mathdoc.fr/item/SM_2004_195_1_a6/
%G en
%F SM_2004_195_1_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Kats V., Beskonechnomernye algebry Li, Mir, M., 1993 | MR | Zbl

[2] Vinberg E. B., “Diskretnye lineinye gruppy, porozhdennye otrazheniyami”, Izv. AN SSSR. Ser. matem., 35 (1971), 1072–1112 | MR | Zbl

[3] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Matem. sb., 30 (72):2 (1952), 349–462 | MR | Zbl

[4] Klimenko E., Sakuma M., “Two-generator discrete subgroups of $\operatorname{Isom}(\mathbb H^2)$ containing orientation-reversing elements”, Geom. Dedicata, 72 (1998), 247–282 | DOI | MR | Zbl

[5] Felikson A., Coxeter decompositions of hyperbolic tetrahedra, Preprint No 98-083, Univ. Bielefeld, Bielefeld, 1998 | MR

[6] Felikson A., “Koksterovskie razbieniya giperbolicheskikh simpleksov”, Matem. sb., 193:12 (2002), 134–156 | MR | Zbl

[7] Vinberg E. B., Shvartsman O. V., “Diskretnye gruppy dvizhenii prostranstv postoyannoi krivizny”, Itogi nauki i tekhniki. Sovr. problemy matem. Fundament. napravleniya, 29, VINITI, M., 1988, 147–259

[8] Kotova I. I., “Opisanie sistem kornei s dannoi gruppoi Veilya”, Matem. zametki, 64:3 (1998), 397–402 | MR | Zbl

[9] Johnson N. W., Kellerhals R., Ratcliffe J. G., Tschantz S. T., “Commensurability classes of hyperbolic Coxeter groups”, Linear Algebra Appl., 345 (2002), 119–147 | DOI | MR | Zbl