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

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

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.

Full text: PDF file (610 kB)
References: PDF file   HTML file

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

Document Type: Article
UDC: 513.6

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
\Bibitem{VavKaz10} \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 \mathnet{http://mi.mathnet.ru/znsl3606} \transl \jour J. Math. Sci. (N. Y.) \yr 2010 \vol 171 \issue 3 \pages 322--330 \crossref{https://doi.org/10.1007/s10958-010-0137-1} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649446591} 

• http://mi.mathnet.ru/eng/znsl3606
• http://mi.mathnet.ru/eng/znsl/v375/p32

 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. N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27
2. 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
3. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550
4. J. Math. Sci. (N. Y.), 219:3 (2016), 355–369
5. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934
6. V. A. Petrov, “Decomposition of transvections: an algebro-geometric approach”, St. Petersburg Math. J., 28:1 (2017), 109–114
•  Number of views: This page: 142 Full text: 43 References: 29