Standard

Towards the reverse decomposition of unipotents. II. The relative case. / Vavilov, N. .

In: ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН, Vol. 484, 2019, p. 5-22.

Research output: Contribution to journal › Article › peer-review

Harvard

Vavilov, N 2019, 'Towards the reverse decomposition of unipotents. II. The relative case', ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН, vol. 484, pp. 5-22. <http://www.pdmi.ras.ru/znsl/2019/v484.html>

APA

Vavilov, N. (2019). Towards the reverse decomposition of unipotents. II. The relative case. ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН, 484, 5-22. http://www.pdmi.ras.ru/znsl/2019/v484.html

Vancouver

Vavilov N. Towards the reverse decomposition of unipotents. II. The relative case. ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН. 2019;484:5-22.

Author

Vavilov, N. . / Towards the reverse decomposition of unipotents. II. The relative case. In: ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН. 2019 ; Vol. 484. pp. 5-22.

BibTeX

@article{a3f3f8ca4eaf4b5d9752cdeeb6c19671,
title = "Towards the reverse decomposition of unipotents. II. The relative case",
abstract = "Recently Raimund Preusser displayed very short polynomial expressions of elementary generators in classical groups over an arbitrary commutative ring as products of conjugates of an arbitrary matrix and its inverse by absolute elementary matrices. In particular, this provides very short proofs for description of normal subgroups. In [27] I discussed various generalisations of these results to exceptional groups, specifically those of types E6 and E7. Here, I produce a further variation of Preusser{\textquoteright}s wonderful idea. Namely, in the case of GL(n, R), n > 4, I obtain similar expressions of elementary transvections as conjugates of g ∈ GL(n, R) and g−1 by relative elementary matrices x ∈ E(n, J) and then x ∈ E(n, R, J), for an ideal J E R. Again, in particular, this allows to give very short proofs for the description of subgroups normalised by E(n, J) or E(n, R, J) – and thus also of subnormal subgroups in GL(n, R).",
keywords = "CLASSICAL GROUPS, Chevalley groups, normal structure, elementary subgroups, decomposition of unipotents, reverse decomposition of unipotents, классические группы, группы Шевалье, структура нормальных подгрупп, элементарные подгруппы, разложение унипотентов, обратное разложение унипотентов",
author = "N. Vavilov",
year = "2019",
language = "English",
volume = "484",
pages = "5--22",
journal = "ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН",
issn = "0373-2703",
publisher = "Санкт-Петербургское отделение Математического института им. В. А. Стеклова РАН",

}

RIS

TY - JOUR

T1 - Towards the reverse decomposition of unipotents. II. The relative case

AU - Vavilov, N.

PY - 2019

Y1 - 2019

N2 - Recently Raimund Preusser displayed very short polynomial expressions of elementary generators in classical groups over an arbitrary commutative ring as products of conjugates of an arbitrary matrix and its inverse by absolute elementary matrices. In particular, this provides very short proofs for description of normal subgroups. In [27] I discussed various generalisations of these results to exceptional groups, specifically those of types E6 and E7. Here, I produce a further variation of Preusser’s wonderful idea. Namely, in the case of GL(n, R), n > 4, I obtain similar expressions of elementary transvections as conjugates of g ∈ GL(n, R) and g−1 by relative elementary matrices x ∈ E(n, J) and then x ∈ E(n, R, J), for an ideal J E R. Again, in particular, this allows to give very short proofs for the description of subgroups normalised by E(n, J) or E(n, R, J) – and thus also of subnormal subgroups in GL(n, R).

AB - Recently Raimund Preusser displayed very short polynomial expressions of elementary generators in classical groups over an arbitrary commutative ring as products of conjugates of an arbitrary matrix and its inverse by absolute elementary matrices. In particular, this provides very short proofs for description of normal subgroups. In [27] I discussed various generalisations of these results to exceptional groups, specifically those of types E6 and E7. Here, I produce a further variation of Preusser’s wonderful idea. Namely, in the case of GL(n, R), n > 4, I obtain similar expressions of elementary transvections as conjugates of g ∈ GL(n, R) and g−1 by relative elementary matrices x ∈ E(n, J) and then x ∈ E(n, R, J), for an ideal J E R. Again, in particular, this allows to give very short proofs for the description of subgroups normalised by E(n, J) or E(n, R, J) – and thus also of subnormal subgroups in GL(n, R).

KW - CLASSICAL GROUPS

KW - Chevalley groups

KW - normal structure

KW - elementary subgroups

KW - decomposition of unipotents

KW - reverse decomposition of unipotents

KW - классические группы

KW - группы Шевалье

KW - структура нормальных подгрупп

KW - элементарные подгруппы

KW - разложение унипотентов

KW - обратное разложение унипотентов

UR - http://ftp.pdmi.ras.ru/znsl/2019/v484/abs005.html

M3 - Article

VL - 484

SP - 5

EP - 22

JO - ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН

JF - ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН

SN - 0373-2703

ER -

ID: 51601868