Coxeter transformations and spectra of operations
Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 345-357 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Coxeter transformations associated with rigged trees are considered. The number $-1$ plays an exceptional role with respect to the spectra of such trees. Systems of generating elements and operations are found in the sets of all rigged trees containing and not containing $-1$ in the spectrum.
@article{SM_2002_193_3_a3,
     author = {V. A. Kolmykov},
     title = {Coxeter transformations and spectra of operations},
     journal = {Sbornik. Mathematics},
     pages = {345--357},
     year = {2002},
     volume = {193},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_3_a3/}
}
TY  - JOUR
AU  - V. A. Kolmykov
TI  - Coxeter transformations and spectra of operations
JO  - Sbornik. Mathematics
PY  - 2002
SP  - 345
EP  - 357
VL  - 193
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_2002_193_3_a3/
LA  - en
ID  - SM_2002_193_3_a3
ER  - 
%0 Journal Article
%A V. A. Kolmykov
%T Coxeter transformations and spectra of operations
%J Sbornik. Mathematics
%D 2002
%P 345-357
%V 193
%N 3
%U http://geodesic.mathdoc.fr/item/SM_2002_193_3_a3/
%G en
%F SM_2002_193_3_a3
V. A. Kolmykov. Coxeter transformations and spectra of operations. Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 345-357. http://geodesic.mathdoc.fr/item/SM_2002_193_3_a3/

[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 (1973), 19–33 | MR

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

[4] 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

[5] Subbotin V. F., Sumin M. V., Issledovanie mnogochlenov, svyazannykh s predstavleniyami grafov, Dep. v VINITI 30.12.82, No 6480-82 Dep., Voronezh. gos. un-t, Voronezh, 1982

[6] Kolmykov V. A., Subbotin V. F., Spektry grafov i kospektralnost, Dep. v VINITI 12.12.83, No 6708-83 Dep., Voronezh. gos. un-t, Voronezh, 1983