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Zap. Nauchn. Sem. POMI, 2010, Volume 375, Pages 32–47 (Mi znsl3606)  

This article is cited in 6 scientific papers (total in 6 papers)

More variations on decomposition of transvections

N. A. Vavilov, V. G. Kazakevich

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: The method of decomposition of unipotents consists in writing elementary matrices as products of factors lying in proper parabolic subgroups, whose images under inner automorphisms also fall into proper parabolic subgroups of certain types. For the general linear group this method was first proposed by Stepanov in 1987 to simplify the proof of Suslin's normality theorem. Soon thereafter Vavilov and Plotkin generalised it to other classical groups and Chevalley groups. Subsequently, many further results of that type have been discovered. In the present paper we describe new versions of decomposition of unipotents, which allow to expand its applicability well beyond the present scope. Here we merely illustrate these ideas for split classical groups, in some simplest cases. Detailed calculations are relegated to subsequent publications. Bibl. – 34 titles.

Key words and phrases: general linear group, elementary subgroup, transvections, decomposition of unipotents, parabolic subgroups, standard description of automorphisms.

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English version:
Journal of Mathematical Sciences (New York), 2010, 171:3, 322–330

Document Type: Article
UDC: 513.6
Received: 08.03.2010

Citation: N. A. Vavilov, V. G. Kazakevich, “More variations on decomposition of transvections”, Problems in the theory of representations of algebras and groups. Part 19, Zap. Nauchn. Sem. POMI, 375, POMI, St. Petersburg, 2010, 32–47; J. Math. Sci. (N. Y.), 171:3 (2010), 322–330

Citation in format AMSBIB
\by N.~A.~Vavilov, V.~G.~Kazakevich
\paper More variations on decomposition of transvections
\inbook Problems in the theory of representations of algebras and groups. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 375
\pages 32--47
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 3
\pages 322--330

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    This publication is cited in the following articles:
    1. N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27  mathnet
    2. N. A. Vavilov, “$\mathrm A_3$-dokazatelstvo strukturnykh teorem dlya grupp Shevalle tipov $\mathrm E_6$$\mathrm E_7$. II. Osnovnaya lemma”, Algebra i analiz, 23:6 (2011), 1–31  mathnet  mathscinet  elib; N. A. Vavilov, “An $\mathrm A_3$-proof of the structure theorems for Chevalley groups of types $\mathrm E_6$ and $\mathrm E_7$. II. The main lemma”, St. Petersburg Math. J., 23:6 (2012), 921–942  crossref  isi  elib
    3. 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
    4. N. A. Vavilov, “Decomposition of unipotents for $\mathrm E_6$ and $\mathrm E_7$: 25 years after”, Voprosy teorii predstavlenii algebr i grupp. 27, Zap. nauchn. sem. POMI, 430, POMI, SPb., 2014, 32–52  mathnet  mathscinet; J. Math. Sci. (N. Y.), 219:3 (2016), 355–369  crossref
    5. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934  mathnet  crossref
    6. V. A. Petrov, “Razlozhenie transvektsii: algebro-geometricheskii podkhod”, Algebra i analiz, 28:1 (2016), 150–157  mathnet  mathscinet  elib; V. A. Petrov, “Decomposition of transvections: an algebro-geometric approach”, St. Petersburg Math. J., 28:1 (2017), 109–114  crossref  isi
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