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 Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 6, Pages 1266–1294 (Mi izv1518)

Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory

V. P. Platonov, V. I. Yanchevskii

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:3, 573–599

Bibliographic databases:

UDC: 512.74+512.552
MSC: 20G15, 12E15, 13A39, 16A54

Citation: V. P. Platonov, V. I. Yanchevskii, “Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984), 1266–1294; Math. USSR-Izv., 25:3 (1985), 573–599

Citation in format AMSBIB
\Bibitem{PlaYan84} \by V.~P.~Platonov, V.~I.~Yanchevskii \paper Dieudonn\'e's conjecture on the structure of unitary groups over a~division ring, and Hermitian $K$-theory \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1984 \vol 48 \issue 6 \pages 1266--1294 \mathnet{http://mi.mathnet.ru/izv1518} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=772116} \zmath{https://zbmath.org/?q=an:0593.16012|0579.16011} \transl \jour Math. USSR-Izv. \yr 1985 \vol 25 \issue 3 \pages 573--599 \crossref{https://doi.org/10.1070/IM1985v025n03ABEH001308} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Pat Morandi, “The Henselization of a valued division algebra”, Journal of Algebra, 122:1 (1989), 232
2. A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of spinor groups”, Math. USSR-Izv., 36:1 (1991), 61–100
3. Bill Jacob, Adrian Wadsworth, “Division algebras over Henselian fields”, Journal of Algebra, 128:1 (1990), 126
4. M. Chacron, “Decomposing and ordering a certain crossed product”, Communications in Algebra, 21:9 (1993), 3197
5. S. I. Adian, E. I. Zel'manov, G. A. Margulis, S. P. Novikov, A. S. Rapinchuk, L. D. Faddeev, V. I. Yanchevskii, “Vladimir Petrovich Platonov (on his 60th birthday)”, Russian Math. Surveys, 55:3 (2000), 601–610
6. R Hazrat, “SK1-like Functors for Division Algebras”, Journal of Algebra, 239:2 (2001), 573
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