Coxeter transformations: Construction of deltoids
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 694-699.

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

The Coxeter transformations associated with deltoids (i.e., with graphs in which all simple cycles have length 3) are considered. The structure of the set of all connected deltoids whose spectra do not contain $-1$ is described.
@article{MZM_2006_79_5_a5,
     author = {V. A. Kolmykov},
     title = {Coxeter transformations: {Construction} of deltoids},
     journal = {Matemati\v{c}eskie zametki},
     pages = {694--699},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a5/}
}
TY  - JOUR
AU  - V. A. Kolmykov
TI  - Coxeter transformations: Construction of deltoids
JO  - Matematičeskie zametki
PY  - 2006
SP  - 694
EP  - 699
VL  - 79
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a5/
LA  - ru
ID  - MZM_2006_79_5_a5
ER  - 
%0 Journal Article
%A V. A. Kolmykov
%T Coxeter transformations: Construction of deltoids
%J Matematičeskie zametki
%D 2006
%P 694-699
%V 79
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a5/
%G ru
%F MZM_2006_79_5_a5
V. A. Kolmykov. Coxeter transformations: Construction of deltoids. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 694-699. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a5/

[1] Burbaki N., Gruppy i algebry Li. Gruppy Kokstera i sistemy Titsa. Gruppy, porozhdennye otrazheniyami. Sistemy kornei, Mir, M., 1972 | MR | Zbl

[2] Bernshtein I. N., Gelfand I. M., Ponomarev V. A., “Funktory Kokstera i teorema Gabrielya”, UMN, 28:2 (170) (1973), 19–33 | MR

[3] Berman S., Lee Y. S., Moody R. V., “The spectrum of a Coxeter transformation, affine Coxeter transformations and the defect map”, J. Algebra, 121 (1989), 339–357 | DOI | MR | Zbl

[4] Coleman A. J., “Killing and the Coxeter transformation of Kac-Moody algebras”, Invent. Math., 95 (1989), 447–477 | DOI | MR | Zbl

[5] Ringel C. M., “The spectral radius of the Coxeter transformations for a generalized Cartan matrix”, Math. Ann., 1994, no. 300, 331–339 | DOI | Zbl

[6] Kolmykov V. A., “Preobrazovaniya Kokstera i geometriya matritsy dannykh”, Matem. sb., 194:7 (2003), 119–126 | MR | Zbl

[7] Kolmykov V. A., “Preobrazovanie Kokstera i chislo "$-1$"”, Matem. sb., 191:10 (2000), 51–56 | MR | Zbl

[8] Kolmykov V. A., “Otrazheniya i trekhmernost”, Matem. zametki, 73:6 (2003), 848–852 | MR | Zbl

[9] Kolmykov V. A., “Preobrazovanie Kokstera i spektry operatsii”, Matem. sb., 193:3 (2002), 37–50 | MR | Zbl

[10] Kolmykov V. A., “Preobrazovanie Kokstera: deltoidy, trilistniki i chisla raspada”, Matem. sb., 196:1 (2005), 67–80 | MR | Zbl

[11] Kolmykov V. A., Menshikh V. V., Subbotin V. F., Sumin M. V., Nekotorye svoistva atsiklicheskikh grafov i svyazannykh s nimi mnogochlenov, Dep. v VINITI 12. 12. 83 No 6707-83 Dep., Voronezh. gos. un-t, Voronezh, 1983