RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. LOMI, 1982, Volume 114, Pages 62–76 (Mi znsl1767)  

This article is cited in 3 scientific papers (total in 3 papers)

Net subgroups of Chevalley groups. II. Gauss decomposition

N. A. Vavilov, E. B. Plotkin


Abstract: This paper is a continuation of RZhMat 1980, 5A439, where there was introduced the subgroup $\Gamma(\sigma)$ of the Chevalley group $G(\Phi, R)$ of type $\Phi$ over a commutative ring $R$ that corresponds to a net $\sigma$, i.e., to a set $\sigma=(\sigma_\alpha)$, $\alpha\in\Phi$, of ideals $\sigma_\alpha$ of $R$ such that $\sigma_\alpha\sigma_\beta\subseteq\sigma_{\alpha+\beta}$ whenever $\alpha,\beta,\alpha+\beta\in\Phi$. It is proved that if the ring $R$ is semilocal, then $\Gamma(\sigma)$ coincides with the group $\Gamma_0(\sigma)$ considered earlier in RZhMat 1976, 10A151; 1977, 10A301; 1978, 6A476. For this purpose there is constructed a decomposition of $\Gamma(\sigma)$ into a product of unipotent subgroups and a torus. Analogous results are obtained for sub-radical nets over an arbitrary commutative ring.

Full text: PDF file (1556 kB)

English version:
Journal of Soviet Mathematics, 1984, 27:4, 2874–2885

Bibliographic databases:

UDC: 513.6

Citation: N. A. Vavilov, E. B. Plotkin, “Net subgroups of Chevalley groups. II. Gauss decomposition”, Modules and algebraic groups, Zap. Nauchn. Sem. LOMI, 114, "Nauka", Leningrad. Otdel., Leningrad, 1982, 62–76; J. Soviet Math., 27:4 (1984), 2874–2885

Citation in format AMSBIB
\Bibitem{VavPlo82}
\by N.~A.~Vavilov, E.~B.~Plotkin
\paper Net subgroups of Chevalley groups.~II. Gauss decomposition
\inbook Modules and algebraic groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 114
\pages 62--76
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1767}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=669560}
\zmath{https://zbmath.org/?q=an:0548.20035|0499.20033}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 27
\issue 4
\pages 2874--2885
\crossref{https://doi.org/10.1007/BF01410741}


Linking options:
  • http://mi.mathnet.ru/eng/znsl1767
  • http://mi.mathnet.ru/eng/znsl/v114/p62

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya gruppy Shevalle tipa $\mathrm F_4$”, Algebra i analiz, 20:4 (2008), 27–63  mathnet  mathscinet  zmath  elib; N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$”, St. Petersburg Math. J., 20:4 (2009), 527–551  crossref  isi
    2. N. A. Vavilov, S. S. Sinchuk, “Parabolicheskie faktorizatsii rasschepimykh klassicheskikh grupp”, Algebra i analiz, 23:4 (2011), 1–30  mathnet  mathscinet  zmath  elib; N. A. Vavilov, S. S. Sinchuk, “Parabolic factorizations of split classical groups”, St. Petersburg Math. J., 23:4 (2012), 637–657  crossref  isi  elib
    3. K. O. Batalkin, N. A. Vavilov, “Parabolicheskie podgruppy $\mathrm{SO}_{2l}$ nad dedekindovym koltsom arifmeticheskogo tipa”, Voprosy teorii predstavlenii algebr i grupp. 23, Zap. nauchn. sem. POMI, 400, POMI, SPb., 2012, 50–69  mathnet  mathscinet; K. O. Batalkin, N. A. Vavilov, “Parabolic subgroups of $\mathrm{SO}_{2l}$ over a Dedekind ring of arithmetic type”, J. Math. Sci. (N. Y.), 192:2 (2013), 154–163  crossref
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:153
    Full text:43

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017