Vinberg's Algorithm for Hyperbolic Lattices
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 769-773.

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

Keywords: hyperbolic lattice, Vinberg's algorithm, reflection group, Coxeter polyhedra.
@article{MZM_2018_103_5_a11,
     author = {N. V. Bogachev and A. Yu. Perepechko},
     title = {Vinberg's {Algorithm} for {Hyperbolic} {Lattices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {769--773},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a11/}
}
TY  - JOUR
AU  - N. V. Bogachev
AU  - A. Yu. Perepechko
TI  - Vinberg's Algorithm for Hyperbolic Lattices
JO  - Matematičeskie zametki
PY  - 2018
SP  - 769
EP  - 773
VL  - 103
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a11/
LA  - ru
ID  - MZM_2018_103_5_a11
ER  - 
%0 Journal Article
%A N. V. Bogachev
%A A. Yu. Perepechko
%T Vinberg's Algorithm for Hyperbolic Lattices
%J Matematičeskie zametki
%D 2018
%P 769-773
%V 103
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a11/
%G ru
%F MZM_2018_103_5_a11
N. V. Bogachev; A. Yu. Perepechko. Vinberg's Algorithm for Hyperbolic Lattices. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 769-773. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a11/

[1] B. A. Venkov, Izv. AN SSSR. Ser. matem., 1:2 (1937), 139–170 | Zbl

[2] F. Esselmann, J. Number Theory, 61:1 (1996), 103–144 | DOI | MR

[3] V. V. Nikulin, Izv. RAN. Ser. matem., 71:1 (2007), 55–60 | DOI | MR | Zbl

[4] E. B. Vinberg, Matem. sb., 87 (129):1 (1972), 18–36 | MR | Zbl

[5] V. O. Bugaenko, Lie Groups, Their Discrete Subgroups, and Invariant Theory, Amer. Math. Soc., Providence, RI, 1992, 33–55 | MR

[6] R. Scharlau, C. Walhorn, Astérisque, 209 (1992), 279–291 | MR

[7] V. V. Nikulin, Tr. MIAN, 230, Nauka, MAIK «Nauka/Interperiodika», M., 2000, 3–255 | MR | Zbl

[8] D. Allcock, The Reflective Lorentzian Lattices of Rank $3$, Mem. Amer. Math. Soc., 220, no. 1033, Amer. Math. Soc., Providence, RI, 2012 | MR

[9] R. Guglielmetti, Hyperbolic Isometries in (In-)Finite Dimensions and Discrete Reflection Groups: Theory and Computations, PhD Thesis, Univ. of Fribourg, 2017

[10] The Sage Mathematics Software System (Version 7.6), 2017 www.sagemath.org

[11] N. Bogachev, A. Perepechko, Vinberg's Algorithm, , 2017 https://github.com/aperep/vinberg-algorithm | DOI

[12] E. B. Vinberg, Tr. MMO, 47, Izd-vo Mosk. un-ta, M., 1984, 68–102 | MR | Zbl

[13] E. B. Vinberg, UMN, 40:1 (241) (1985), 29–66 | MR | Zbl

[14] R. Guglielmetti, LMS J. Comput. Math., 18:1 (2015), 754–773 | DOI | MR

[15] C. Walhorn, Arithmetische Spiegelungsgruppen auf dem $4$-dimensionalen hyperbolischen Raum, PhD Thesis, Univ. of Bielefeld, 1993

[16] E. B. Vinberg, Tr. MMO, 68, Izd-vo Mosk. un-ta, M., 2007, 44–76 | MR

[17] N. V. Bogachev, Reflective Anisotropic Hyperbolic Lattices of Rank $4$, 2016, arXiv: 1610.06148v1

[18] N. V. Bogachev, UMN, 72:1 (433) (2017), 193–194 | DOI | MR