RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb. (N.S.), 1976, Volume 100(142), Number 2(6), Pages 191–200 (Mi msb2869)

The infinitude of the reduced Whitehead group in the Tannaka–Artin problem

V. P. Platonov

Abstract: Using the methods and results of preceding papers of the author (V. P. Platonov, The Tarmaka–Artin problem and groups of projective conorms, Dokl. Akad. Nauk SSSR, 222, № 6 (1975), 1229–1302; The Tarmaka–Artin problem and reduced $K$-theory, Izv. Akad. Nauk SSSR, Ser. Mat., 40, № 2 (1976), 227–261), in the first part of this paper we find conditions under which the reduced Whitehead group is infinite, and in the second, larger part we give the solution of the Tannaka–Artin problem for cyclic algebras. In particular, we completely calculate the reduced Whitehead group $SK_1(A)$ for cyclic algebras $A$ over formal power series fields and construct cyclic algebras of arbitrary degree $n^2$ with Whitehead group that is arbitrarily large but finite, and also with infinite Whitehead group.
Bibliography: 15 titles.

Full text: PDF file (1186 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1976, 29:2, 167–176

Bibliographic databases:

UDC: 513.6
MSC: Primary 16A40, 16A18, 12A60, 12A65; Secondary 18F25

Citation: V. P. Platonov, “The infinitude of the reduced Whitehead group in the Tannaka–Artin problem”, Mat. Sb. (N.S.), 100(142):2(6) (1976), 191–200; Math. USSR-Sb., 29:2 (1976), 167–176

Citation in format AMSBIB
\Bibitem{Pla76} \by V.~P.~Platonov \paper The infinitude of the reduced Whitehead group in the Tannaka--Artin problem \jour Mat. Sb. (N.S.) \yr 1976 \vol 100(142) \issue 2(6) \pages 191--200 \mathnet{http://mi.mathnet.ru/msb2869} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=412228} \zmath{https://zbmath.org/?q=an:0352.16009} \transl \jour Math. USSR-Sb. \yr 1976 \vol 29 \issue 2 \pages 167--176 \crossref{https://doi.org/10.1070/SM1976v029n02ABEH003660} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EZ91500003} 

• http://mi.mathnet.ru/eng/msb2869
• http://mi.mathnet.ru/eng/msb/v142/i2/p191

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Yanchevskii, “Reduced unitary $K$-theory and division rings over discretely valued Hensel fields”, Math. USSR-Izv., 13:1 (1979), 175–213
2. V. I. Yanchevskii, “Reduced unitary $K$-theory. Aplications to algebraic groups”, Math. USSR-Sb., 38:4 (1981), 533–548
3. A. E. Zalesskii, “Linear groups”, Russian Math. Surveys, 36:5 (1981), 63–128
4. Yu. L. Ershov, “Henselian valuations of division rings and the group $SK_1$”, Math. USSR-Sb., 45:1 (1983), 63–71
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. Hazrat R. Wadsworth A.R., “Unitary Sk1 of Graded and Valued Division Algebras”, Proc. London Math. Soc., 103:Part 3 (2011), 508–534
7. Hazrat R. Wadsworth A.R., “Sk1 of Graded Division Algebras”, Isr. J. Math., 183:1 (2011), 117–163
8. A. R. Wadsworth, “Unitary SK1 of semiramified graded and valued division algebras”, manuscripta math, 139:3-4 (2012), 343
•  Number of views: This page: 244 Full text: 45 References: 24 First page: 2