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Unitary Steinberg group is centrally closed. / Lavrenov, A.

в: St. Petersburg Mathematical Journal, Том 24, № 5, 2013, стр. 783--794.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Lavrenov, A 2013, 'Unitary Steinberg group is centrally closed', St. Petersburg Mathematical Journal, Том. 24, № 5, стр. 783--794. <http://www.ams.org/journals/spmj/2013-24-05/S1061-0022-2013-01265-9/S1061-0022-2013-01265-9.pdf>

APA

Lavrenov, A. (2013). Unitary Steinberg group is centrally closed. St. Petersburg Mathematical Journal, 24(5), 783--794. http://www.ams.org/journals/spmj/2013-24-05/S1061-0022-2013-01265-9/S1061-0022-2013-01265-9.pdf

Vancouver

Lavrenov A. Unitary Steinberg group is centrally closed. St. Petersburg Mathematical Journal. 2013;24(5):783--794.

Author

Lavrenov, A. / Unitary Steinberg group is centrally closed. в: St. Petersburg Mathematical Journal. 2013 ; Том 24, № 5. стр. 783--794.

BibTeX

@article{cf6bcc2a9a79402f95a57e96bf070590,
title = "Unitary Steinberg group is centrally closed",
abstract = "Let (R,Lambda) be an arbitrary form ring, U(2n,R,Lambda) be the hyperbolic unitary group, EU(2n,R,Lambda) be its elementary subgroup and StU(2n,R,Lambda) be the unitary Steinberg group. We prove that under natural assumption n>=5 every central extension of StU(2n,R,Lambda) splits. Using this result in the situation when the kernel of natural epimorphism from StU(2n,R,Lambda) onto EU(2n,R,Lambda) is contained in the center of StU(2n,R,Lambda) we obtain that this kernel coincides with the Schur multiplier of the elementary unitary group. We use Steinberg relation from the paper~[10] to obtain the most simple proofs of these results.",
keywords = "Unitary Steinberg group, Schur multiplier, unitary group, form parameter, non-stable K-theory",
author = "A. Lavrenov",
year = "2013",
language = "не определен",
volume = "24",
pages = "783----794",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "5",

}

RIS

TY - JOUR

T1 - Unitary Steinberg group is centrally closed

AU - Lavrenov, A.

PY - 2013

Y1 - 2013

N2 - Let (R,Lambda) be an arbitrary form ring, U(2n,R,Lambda) be the hyperbolic unitary group, EU(2n,R,Lambda) be its elementary subgroup and StU(2n,R,Lambda) be the unitary Steinberg group. We prove that under natural assumption n>=5 every central extension of StU(2n,R,Lambda) splits. Using this result in the situation when the kernel of natural epimorphism from StU(2n,R,Lambda) onto EU(2n,R,Lambda) is contained in the center of StU(2n,R,Lambda) we obtain that this kernel coincides with the Schur multiplier of the elementary unitary group. We use Steinberg relation from the paper~[10] to obtain the most simple proofs of these results.

AB - Let (R,Lambda) be an arbitrary form ring, U(2n,R,Lambda) be the hyperbolic unitary group, EU(2n,R,Lambda) be its elementary subgroup and StU(2n,R,Lambda) be the unitary Steinberg group. We prove that under natural assumption n>=5 every central extension of StU(2n,R,Lambda) splits. Using this result in the situation when the kernel of natural epimorphism from StU(2n,R,Lambda) onto EU(2n,R,Lambda) is contained in the center of StU(2n,R,Lambda) we obtain that this kernel coincides with the Schur multiplier of the elementary unitary group. We use Steinberg relation from the paper~[10] to obtain the most simple proofs of these results.

KW - Unitary Steinberg group

KW - Schur multiplier

KW - unitary group

KW - form parameter

KW - non-stable K-theory

M3 - статья

VL - 24

SP - 783

EP - 794

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 5676281