The Coxeter transformation: deltoids, trefoils, and decay numbers
Sbornik. Mathematics, Tome 196 (2005) no. 1, pp. 63-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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Coxeter transformations associated with deltoids (that is, graphs with the lengths of all simple cycles equal to 3) are considered. All irreducible objects in the set of all connected deltoids with spectrum containing -1 are described and a system of generating elements and operations is found. One formalization of the concept of “critical decay number” is discussed.
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V. A. Kolmykov. The Coxeter transformation: deltoids, trefoils, and decay numbers. Sbornik. Mathematics, Tome 196 (2005) no. 1, pp. 63-75. http://geodesic.mathdoc.fr/item/SM_2005_196_1_a2/

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

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

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

[6] Manin Yu. I., A course in mathematical logic, Springer-Verlag, New York, 1977 | MR | Zbl

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

[8] Kolmykov V. A., “Nulevoi konus formy Kartana–Titsa i grafy Dynkina”, Sbornik trudov seminara I. R. Shafarevicha, no. 2, Fond matem. obraz. i prosvesch., M., 2000, 3–14