Standard

Multiple commutators of elementary subgroups: end of the line. / Vavilov, Nikolai; Zhang, Zuhong.

In: Linear Algebra and Its Applications, Vol. 599, 15.08.2020, p. 1-17.

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

Harvard

Vavilov, N & Zhang, Z 2020, 'Multiple commutators of elementary subgroups: end of the line', Linear Algebra and Its Applications, vol. 599, pp. 1-17. https://doi.org/10.1016/j.laa.2020.03.044

APA

Vavilov, N., & Zhang, Z. (2020). Multiple commutators of elementary subgroups: end of the line. Linear Algebra and Its Applications, 599, 1-17. https://doi.org/10.1016/j.laa.2020.03.044

Vancouver

Vavilov N, Zhang Z. Multiple commutators of elementary subgroups: end of the line. Linear Algebra and Its Applications. 2020 Aug 15;599:1-17. https://doi.org/10.1016/j.laa.2020.03.044

Author

Vavilov, Nikolai ; Zhang, Zuhong. / Multiple commutators of elementary subgroups: end of the line. In: Linear Algebra and Its Applications. 2020 ; Vol. 599. pp. 1-17.

BibTeX

@article{7f67080138cb4713ab826cae8b30c268,
title = "Multiple commutators of elementary subgroups: end of the line",
abstract = "In our previous joint papers with Roozbeh Hazrat and Alexei Stepanov we established commutator formulas for relative elementary subgroups in , , and other similar groups, such as Bak's unitary groups, or Chevalley groups. In particular, there it was shown that multiple commutators of elementary subgroups can be reduced to double such commutators. However, since the proofs of these results depended on the standard commutator formulas, it was assumed that the ground ring R is quasi-finite. Here we propose a different approach which allows to lift any such assumptions and establish almost definitive results. In particular, we prove multiple commutator formulas, and other related facts for over an arbitrary associative ring R.",
keywords = "math.RA, General linear group, congruence subgroups, elementary subgroups, standard commutator formulae, Elementary subgroups, Standard commutator formulae, Congruence subgroups, GL(N,A)",
author = "Nikolai Vavilov and Zuhong Zhang",
note = "14 pages. arXiv admin note: text overlap with arXiv:1910.08984",
year = "2020",
month = aug,
day = "15",
doi = "10.1016/j.laa.2020.03.044",
language = "English",
volume = "599",
pages = "1--17",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Multiple commutators of elementary subgroups: end of the line

AU - Vavilov, Nikolai

AU - Zhang, Zuhong

N1 - 14 pages. arXiv admin note: text overlap with arXiv:1910.08984

PY - 2020/8/15

Y1 - 2020/8/15

N2 - In our previous joint papers with Roozbeh Hazrat and Alexei Stepanov we established commutator formulas for relative elementary subgroups in , , and other similar groups, such as Bak's unitary groups, or Chevalley groups. In particular, there it was shown that multiple commutators of elementary subgroups can be reduced to double such commutators. However, since the proofs of these results depended on the standard commutator formulas, it was assumed that the ground ring R is quasi-finite. Here we propose a different approach which allows to lift any such assumptions and establish almost definitive results. In particular, we prove multiple commutator formulas, and other related facts for over an arbitrary associative ring R.

AB - In our previous joint papers with Roozbeh Hazrat and Alexei Stepanov we established commutator formulas for relative elementary subgroups in , , and other similar groups, such as Bak's unitary groups, or Chevalley groups. In particular, there it was shown that multiple commutators of elementary subgroups can be reduced to double such commutators. However, since the proofs of these results depended on the standard commutator formulas, it was assumed that the ground ring R is quasi-finite. Here we propose a different approach which allows to lift any such assumptions and establish almost definitive results. In particular, we prove multiple commutator formulas, and other related facts for over an arbitrary associative ring R.

KW - math.RA

KW - General linear group

KW - congruence subgroups

KW - elementary subgroups

KW - standard commutator formulae

KW - Elementary subgroups

KW - Standard commutator formulae

KW - Congruence subgroups

KW - GL(N,A)

UR - http://www.scopus.com/inward/record.url?scp=85082776648&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/27a7f415-1a12-35ff-a846-7807fbb1f1fe/

U2 - 10.1016/j.laa.2020.03.044

DO - 10.1016/j.laa.2020.03.044

M3 - Article

VL - 599

SP - 1

EP - 17

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 51600955