Overgroups of exterior powers of an elementary group. Normalizers

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Overgroups of exterior powers of an elementary group. Normalizers. / Lubkov, R.; Nekrasov, I.

In: Documenta Mathematica, Vol. 29, No. 5, 25.09.2024, p. 1243-1268.

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

BibTeX

@article{9333af365775446ea67ff28113beb59c,

title = "Overgroups of exterior powers of an elementary group. Normalizers",

abstract = "We establish two characterizations of an algebraic group scheme GLn over Z. Geo-metrically, the schemeVm GLn is a stabilizer of an explicitly given invariant form or, generally, an invariant ideal of forms. Algebraically,Vm GLn is isomorphic (as a scheme over Z) to a normalizer of the elementary subgroup functorVm En and a normalizer of the subschemeVm SLn. Our immediate goal is to apply both descriptions in the “sandwich classification” of overgroups of the elementary subgroup. Additionally, the results can be seen as a solution of the linear preserver problem for algebraic group schemes over Z, providing a more functorial description that goes beyond geometry of the classical case over fields. {\textcopyright} 2024 Deutsche Mathematiker-Vereinigung.",

keywords = "elementary subgroup, exterior power, general linear group, invariant forms, linear preserver problems, Plucker polynomials",

author = "R. Lubkov and I. Nekrasov",

note = "Export Date: 21 October 2024 Сведения о финансировании: Ministry of Education and Science of the Russian Federation, Minobrnauka, 075–15–2022–287 Текст о финансировании 1: Funding. The first author is supported by \u201CNative towns\u201D, a social investment program of PJSC \u201CGazprom Neft\u201D and by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075\u201315\u20132022\u2013287).",

year = "2024",

month = sep,

day = "25",

doi = "10.4171/dm/956",

language = "Английский",

volume = "29",

pages = "1243--1268",

journal = "Documenta Mathematica",

issn = "1431-0635",

publisher = "Deutsche Mathematiker Vereinigung",

number = "5",

}

RIS

TY - JOUR

T1 - Overgroups of exterior powers of an elementary group. Normalizers

AU - Lubkov, R.

AU - Nekrasov, I.

N1 - Export Date: 21 October 2024 Сведения о финансировании: Ministry of Education and Science of the Russian Federation, Minobrnauka, 075–15–2022–287 Текст о финансировании 1: Funding. The first author is supported by \u201CNative towns\u201D, a social investment program of PJSC \u201CGazprom Neft\u201D and by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075\u201315\u20132022\u2013287).

PY - 2024/9/25

Y1 - 2024/9/25

N2 - We establish two characterizations of an algebraic group scheme GLn over Z. Geo-metrically, the schemeVm GLn is a stabilizer of an explicitly given invariant form or, generally, an invariant ideal of forms. Algebraically,Vm GLn is isomorphic (as a scheme over Z) to a normalizer of the elementary subgroup functorVm En and a normalizer of the subschemeVm SLn. Our immediate goal is to apply both descriptions in the “sandwich classification” of overgroups of the elementary subgroup. Additionally, the results can be seen as a solution of the linear preserver problem for algebraic group schemes over Z, providing a more functorial description that goes beyond geometry of the classical case over fields. © 2024 Deutsche Mathematiker-Vereinigung.

AB - We establish two characterizations of an algebraic group scheme GLn over Z. Geo-metrically, the schemeVm GLn is a stabilizer of an explicitly given invariant form or, generally, an invariant ideal of forms. Algebraically,Vm GLn is isomorphic (as a scheme over Z) to a normalizer of the elementary subgroup functorVm En and a normalizer of the subschemeVm SLn. Our immediate goal is to apply both descriptions in the “sandwich classification” of overgroups of the elementary subgroup. Additionally, the results can be seen as a solution of the linear preserver problem for algebraic group schemes over Z, providing a more functorial description that goes beyond geometry of the classical case over fields. © 2024 Deutsche Mathematiker-Vereinigung.

KW - elementary subgroup

KW - exterior power

KW - general linear group

KW - invariant forms

KW - linear preserver problems

KW - Plucker polynomials

U2 - 10.4171/dm/956

DO - 10.4171/dm/956

M3 - статья

VL - 29

SP - 1243

EP - 1268

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

IS - 5

ER -

ID: 126219016