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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 423, Pages 244–263 (Mi znsl6006)  
This article is cited in 11 scientific papers (total in 11 papers)

Non-Abelian $K$-theory for Chevalley groups over rings

A. V. Stepanovab

a St. Petersburg Electrotechnical University, St. Petersburg, Russia
b St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
Full-text PDF (268 kB) Citations (11)
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Abstract: We announce some results on the structure of Chevalley groups $G(R)$ over a commutative ring $R$ recently obtained by the author. The following results are generalized and improved:
(1) Relative local-global principle.
(2) Generators of relative elementary subgroups.
(3) Relative multi-commutator formulas.
(4) Nilpotent structure of relative $\mathrm K_1$.
(5) Boundedness of commutator length.
\noindent The proof of first two items is based on computations with generators of the elementary subgroups translated into the language of parabolic subgroups. For the proof of the further ones we enlarge the relative elementary subgroup, construct a generic element, and use localization in a universal ring.
Key words and phrases: Chevalley group, principal congruence subgroup, local-global principle, commutator formula, elementary subgroup, commutator width.
Received: 02.12.2013
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 4, Pages 645–656
DOI: https://doi.org/10.1007/s10958-015-2518-y
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: Russian
Citation: A. V. Stepanov, “Non-Abelian $K$-theory for Chevalley groups over rings”, Problems in the theory of representations of algebras and groups. Part 26, Zap. Nauchn. Sem. POMI, 423, POMI, St. Petersburg, 2014, 244–263; J. Math. Sci. (N. Y.), 209:4 (2015), 645–656
Citation in format AMSBIB
\Bibitem{Ste14}
\by A.~V.~Stepanov
\paper Non-Abelian $K$-theory for Chevalley groups over rings
\inbook Problems in the theory of representations of algebras and groups. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 423
\pages 244--263
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3480699}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 4
\pages 645--656
\crossref{https://doi.org/10.1007/s10958-015-2518-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84943358367}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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