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Nonabelian K-theory for Chevalley groups over rings. / Stepanov, A.

In: Journal of Mathematical Sciences, Vol. 209, No. 4, 2015, p. 645-656.

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

Harvard

Stepanov, A 2015, 'Nonabelian K-theory for Chevalley groups over rings', Journal of Mathematical Sciences, vol. 209, no. 4, pp. 645-656. https://doi.org/10.1007/s10958-015-2518-y

APA

Stepanov, A. (2015). Nonabelian K-theory for Chevalley groups over rings. Journal of Mathematical Sciences, 209(4), 645-656. https://doi.org/10.1007/s10958-015-2518-y

Vancouver

Stepanov A. Nonabelian K-theory for Chevalley groups over rings. Journal of Mathematical Sciences. 2015;209(4):645-656. https://doi.org/10.1007/s10958-015-2518-y

Author

Stepanov, A. / Nonabelian K-theory for Chevalley groups over rings. In: Journal of Mathematical Sciences. 2015 ; Vol. 209, No. 4. pp. 645-656.

BibTeX

@article{4a85f6a124da4f5fb0ab77f50a697460,
title = "Nonabelian K-theory for Chevalley groups over rings",
abstract = "Results on structure of a Chevalley group $G(R)$ over a ring $R$ obtained recently by the author are anounced. The following results are generalized and improved. (1) Relative local-global principle. (2) Generators of relative elementary subgroups. (3) Relative multi-commutator formulas. (4) Nilpotent structure of relative $\K_1$; (5) Boundedness of commutator length. The proof of first two items is based on computations with generators of the elementary subgroups translated to the language of parabolic subgroups. For the proof of the others we enlarge relative elementary subgroup, construct a generic element, and use localization in a universal ring.",
author = "A. Stepanov",
year = "2015",
doi = "10.1007/s10958-015-2518-y",
language = "English",
volume = "209",
pages = "645--656",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Nonabelian K-theory for Chevalley groups over rings

AU - Stepanov, A.

PY - 2015

Y1 - 2015

N2 - Results on structure of a Chevalley group $G(R)$ over a ring $R$ obtained recently by the author are anounced. The following results are generalized and improved. (1) Relative local-global principle. (2) Generators of relative elementary subgroups. (3) Relative multi-commutator formulas. (4) Nilpotent structure of relative $\K_1$; (5) Boundedness of commutator length. The proof of first two items is based on computations with generators of the elementary subgroups translated to the language of parabolic subgroups. For the proof of the others we enlarge relative elementary subgroup, construct a generic element, and use localization in a universal ring.

AB - Results on structure of a Chevalley group $G(R)$ over a ring $R$ obtained recently by the author are anounced. The following results are generalized and improved. (1) Relative local-global principle. (2) Generators of relative elementary subgroups. (3) Relative multi-commutator formulas. (4) Nilpotent structure of relative $\K_1$; (5) Boundedness of commutator length. The proof of first two items is based on computations with generators of the elementary subgroups translated to the language of parabolic subgroups. For the proof of the others we enlarge relative elementary subgroup, construct a generic element, and use localization in a universal ring.

U2 - 10.1007/s10958-015-2518-y

DO - 10.1007/s10958-015-2518-y

M3 - Article

VL - 209

SP - 645

EP - 656

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 5738611