Geodesic
Coxeter transformations and the geometry of the data matrix
Sbornik. Mathematics, Tome 194 (2003) no. 7, pp. 1069-1077 
V. A. Kolmykov. Coxeter transformations and the geometry of the data matrix. Sbornik. Mathematics, Tome 194 (2003) no. 7, pp. 1069-1077. http://geodesic.mathdoc.fr/item/SM_2003_194_7_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Coxeter conjugation of an arbitrary set of square matrices is introduced and David matrices are defined. It is proved that the Coxeter conjugate of the set of all complex symmetric matrices coincides with the set of all complex David matrices.

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

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

[3] Kolmykov V. A., “Preobrazovanie Kokstera i kvazikolchany”, Matem. zametki, 72:3 (2002), 472–473 | MR | Zbl

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

[5] Dlab V., Ringel C. M., Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc., 173, Amer. Math. Soc., Providence, RI, 1976 | MR

[6] Dlab V., Ringel C. M., “On algebras of finite representation type”, J. Algebra, 33 (1978), 306–394 | DOI | MR

[7] Ringel C. M., “Representations of K-species and bimodules”, J. Algebra, 41 (1978), 269–302 | DOI | MR