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Zap. Nauchn. Sem. POMI, 2010, Volume 375, Pages 48–60 (Mi znsl3607)  

This article is cited in 5 scientific papers (total in 5 papers)

Dennis–Vaserstein type decompositions

N. A. Vavilov, S. S. Sinchuk

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: We prove a generalisation of Dennis–Vaserstein decomposition for an arbitrary pair of maximal parabolic subgroups $P_r$ and $P_s$ in the general linear group $\mathrm{GL}(n,R)$, provided that $r-s\geq\mathrm{sr}(R)$. The usual Dennis–Vaserstein decomposition is the special case where $r=n-1$, $s=1$. Bibl. – 23 titles.

Key words and phrases: general linear group, lementary subgroup, parabolic subgroups, stable rank, Dennis–Vaserstein decomposition.

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English version:
Journal of Mathematical Sciences (New York), 2010, 171:3, 331–337

Document Type: Article
UDC: 513.6
Received: 13.03.2010

Citation: N. A. Vavilov, S. S. Sinchuk, “Dennis–Vaserstein type decompositions”, Problems in the theory of representations of algebras and groups. Part 19, Zap. Nauchn. Sem. POMI, 375, POMI, St. Petersburg, 2010, 48–60; J. Math. Sci. (N. Y.), 171:3 (2010), 331–337

Citation in format AMSBIB
\Bibitem{VavSin10}
\by N.~A.~Vavilov, S.~S.~Sinchuk
\paper Dennis--Vaserstein type decompositions
\inbook Problems in the theory of representations of algebras and groups. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 375
\pages 48--60
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3607}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 3
\pages 331--337
\crossref{https://doi.org/10.1007/s10958-010-0138-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649444590}


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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. N. A. Vavilov, A. V. Smolenskii, B. Suri, “Unitreugolnye faktorizatsii grupp Shevalle”, Voprosy teorii predstavlenii algebr i grupp. 21, Zap. nauchn. sem. POMI, 388, POMI, SPb., 2011, 17–47  mathnet; N. A. Vavilov, A. V. Smolensky, B. Sury, “Unitriangular factorisations of Chevalley groups”, J. Math. Sci. (N. Y.), 183:5 (2012), 584–599  crossref
    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. N. A. Vavilov, E. I. Kovach, “$\mathrm{SL}_2$-faktorizatsii grupp Shevalle”, Voprosy teorii predstavlenii algebr i grupp. 22, Zap. nauchn. sem. POMI, 394, POMI, SPb., 2011, 20–32  mathnet  mathscinet; N. A. Vavilov, E. I. Kovach, “$\mathrm{SL}_2$-factorisations of Chevalley groups”, J. Math. Sci. (N. Y.), 188:5 (2013), 483–489  crossref
    4. N. A. Vavilov, A. V. Stepanov, “Lineinye gruppy nad obschimi koltsami I. Obschie mesta”, Voprosy teorii predstavlenii algebr i grupp. 22, Zap. nauchn. sem. POMI, 394, POMI, SPb., 2011, 33–139  mathnet  mathscinet; N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  crossref
    5. K. B. Tsvetkov, “Parabolicheskie faktorizatsii matrichnogo koltsa”, Voprosy teorii predstavlenii algebr i grupp. 24, Zap. nauchn. sem. POMI, 413, POMI, SPb., 2013, 219–227  mathnet  mathscinet; K. B. Tsvetkov, “Parabolic factorization for a matrix ring”, J. Math. Sci. (N. Y.), 202:3 (2014), 479–484  crossref
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