Geodesic
Discrete linear groups generated by reflections
Izvestiya. Mathematics, Tome 5 (1971) no. 5, pp. 1083-1119 
È. B. Vinberg. Discrete linear groups generated by reflections. Izvestiya. Mathematics, Tome 5 (1971) no. 5, pp. 1083-1119. http://geodesic.mathdoc.fr/item/IM2_1971_5_5_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate linear groups generated by reflections in the faces of a convex polyhedral cone and operating discretely on an open convex cone. These groups generalize the discrete groups of motions in simply connected spaces of constant curvature, generated by reflection. Like the latter, they turn out to be Coxeter groups.

[1] Coxeter H. S. M., “Discrete groups generated by reflections”, Ann. Math., 35:3 (1934), 588–621 | DOI | MR | Zbl

[2] Coxeter H. S. M., “The complete enumeration of finite groups of the form $R^2_i= (R_iR_j)^{k_{ij}}=1$”, J. London Math. Soc., 10:1 (1935), 21–25 | DOI | MR | Zbl

[3] Tits J., Groups et géométries de Coxeter. Notes polycopiées, IHES, Paris, 1961

[4] Bourbaki N., Élements de mathématiques. Fasc. XXXIV. Groupes et algèbres de Lie., Paris, 1968

[5] Makarov V. S., “Ob odnom klasse razbienii prostranstva Lobachevskogo”, Dokl. AN SSSR, 161:2 (1965), 277–278 | MR | Zbl

[6] Makarov V. S., “Ob odnom klasse diskretnykh grupp prostranstva Lobachevskogo, imeyuschikh beskonechnuyu fundamentalnuyu oblast konechnoi mery”, Dokl. AN SSSR, 167:1 (1966), 30–33 | MR | Zbl

[7] Vinberg E. B., Kats V. G., “Kvaziodnorodnye konusy”, Matem. zametki, 1:3 (1967), 347–354 | MR | Zbl

[8] Vinberg E. B., “Diskretnye gruppy, porozhdennye otrazheniyami, v prostranstvakh Lobachevskogo”, Matem. sb., 72:3 (1967), 471–488 | MR | Zbl

[9] Vinberg E. B., “Nekotorye primery kristallograficheskikh grupp v prostranstvakh Lobachevskogo”, Matem. sb., 78:4 (1969), 633–639 | MR | Zbl

[10] Vinberg E. B., “Geometricheskie predstavleniya grupp Koksetera”, Uspekhi matem. nauk, 25:2 (1970), 267–268 | MR | Zbl

[11] Andreev E. M., “O vypuklykh mnogogrannikakh v prostranstvakh Lobachevskogo”, Matem. sb., 81(123) (1970), 445–478 | Zbl

[12] Andreev E. M., “O vypuklykh mnogogrannikakh konechnogo ob'ema v prostranstve Lobachevskogo”, Matem. sb., 83(125) (1970), 256–260 | Zbl

[13] Andreev E. M., “O peresechenii ploskostei granei mnogogrannikov s ostrymi uglami”, Matem. zametki, 8:4 (1970), 521–527 | Zbl

[14] Makarov V. S., “O fedorovskikh gruppakh 4-mernogo i 5-mernogo prostranstv Lobachevskogo”, Issledovaniya po obschei algebre, Kishinevskii un-t, 1970, 120–128