Geodesic
Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory
Izvestiya. Mathematics, Tome 25 (1985) no. 3, pp. 573-599 Cet article a éte moissonné depuis la source Math-Net.Ru

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A multiplicative theory of finite-dimensional division rings with involutions of the first kind is developed in connection with Dieudonné's conjecture, and the structure of arbitrary division rings over Henselian fields is studied. The unitary Whitehead group $UK_1(\tau,A)$ is computed for Henselian division rings $A$ with an involution $\tau$. Classes of division rings for which Dieudonné's conjecture has an affirmative answer are exhibited. Bibliography: 17 titles. 
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     title = {Dieudonn\'e's conjecture on the structure of unitary groups over a~division ring, and {Hermitian} $K$-theory},
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V. P. Platonov; V. I. Yanchevskii. Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory. Izvestiya. Mathematics, Tome 25 (1985) no. 3, pp. 573-599. http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a8/

[1] Dieudonne J., “On the structure of unitary groups”, Trans. Amer. Math. Soc., 72 (1952), 367–385 | DOI | MR | Zbl

[2] Wall G. E., “The structure of a unitary group”, Publ. Math. IHES, 1 (1959), 3–24 | MR

[3] Dedonne Zh., Geometriya klassicheskikh grupp, Mir, M., 1974 | MR

[4] Platonov V. P., Yanchevskii V. I., “Struktura unitarnykh grupp i kommutant prostoi algebry nad globalnymi polyami”, DAN SSSR, 208:3 (1973), 541–544 | MR | Zbl

[5] Platonov V. P., “Gipoteza Dedonne i nesyur'ektivnost nakrytii algebraicheskikh grupp na $k$-tochkakh”, DAN SSSR, 216:5, 986–980 | MR

[6] Platonov V. Ya., “Problemy Tannaka–Artina i privedennaya $K$-teoriya”, Izv. AN SSSR. Ser. matem., 40:2 (1976), 227–261 | MR | Zbl

[7] Platonov V. P., “Privedennaya $K$-teoriya i approksimatsiya v algebraicheskikh gruppakh”, Trudy Mat. in-ta AN SSSR, 142, 1976, 198–207 | MR | Zbl

[8] Yanchevskii V. I., “Privedennaya unitarnaya $K$-teoriya i tela nad genzelevymi diskretno normirovannymi polyami”, Izv. AN SSSR. Ser. matem., 42:4 (1978), 879–918 | MR

[9] Yanchevskii V. I., “Privedennaya unitarnaya $K$-teoriya. Prilozheniya k algebraicheskim gruppam”, Matem. sb., 110:4 (1979), 579–596 | MR

[10] Tits J., “Groupes de Whitehead de groupes algebriques simples”, d'apres V. P. Platonov et al. (Seminaire Bourbaki, June, 1977), Lecture Notes in Mathematics, 677, 1978, 218–236 | MR | Zbl

[11] Albert A., Structure of Algebras, New York, 1939

[12] Burbaki N., Algebra: Moduli, koltsa, formy, Nauka, M., 1966 | MR

[13] Shilling O. F., “The Theory of Valuations”, Amer. Math. Soc., 17 (1950), 1–253 | MR

[14] Rowen L. H., “Central simple algebras”, Israel J. Math., 29 (1978), 285–301 | DOI | MR | Zbl

[15] Artin E., Geometricheskaya algebra, Nauka, M., 1969 | MR | Zbl

[16] Draxl P., Kneser M., $SK_1$ von Schiefkörpern, Lect. Notes in Math., 778, Springer-Verlag, 1980 | MR | Zbl

[17] Algebraicheskaya teoriya chisel, Mir, M., 1969 | MR