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Centrality of K_2-functor revisited. / Voronetsky, Egor.

In: Journal of Pure and Applied Algebra, Vol. 225, No. 4, 106547, 01.04.2021.

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

Harvard

Voronetsky, E 2021, 'Centrality of K_2-functor revisited', Journal of Pure and Applied Algebra, vol. 225, no. 4, 106547. https://doi.org/10.1016/j.jpaa.2020.106547

APA

Voronetsky, E. (2021). Centrality of K_2-functor revisited. Journal of Pure and Applied Algebra, 225(4), [106547]. https://doi.org/10.1016/j.jpaa.2020.106547

Vancouver

Voronetsky E. Centrality of K_2-functor revisited. Journal of Pure and Applied Algebra. 2021 Apr 1;225(4). 106547. https://doi.org/10.1016/j.jpaa.2020.106547

Author

Voronetsky, Egor. / Centrality of K_2-functor revisited. In: Journal of Pure and Applied Algebra. 2021 ; Vol. 225, No. 4.

BibTeX

@article{624f5dafdb2744559318d9dce2d6f454,
title = "Centrality of K_2-functor revisited",
abstract = "We prove that St(n,A) is a crossed module over GL(n,A) under a local stable rank condition on an algebra A over a commutative ring. Our proof uses only elementary localization techniques in terms of pro-groups and stability results for K1 and K2. We also prove similar result for the Steinberg group associated with any sufficiently isotropic general linear group constructed by a quasi-finite algebra.",
keywords = "Crossed module, Isotropic linear group, Steinberg group",
author = "Egor Voronetsky",
year = "2021",
month = apr,
day = "1",
doi = "10.1016/j.jpaa.2020.106547",
language = "English",
volume = "225",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Centrality of K_2-functor revisited

AU - Voronetsky, Egor

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We prove that St(n,A) is a crossed module over GL(n,A) under a local stable rank condition on an algebra A over a commutative ring. Our proof uses only elementary localization techniques in terms of pro-groups and stability results for K1 and K2. We also prove similar result for the Steinberg group associated with any sufficiently isotropic general linear group constructed by a quasi-finite algebra.

AB - We prove that St(n,A) is a crossed module over GL(n,A) under a local stable rank condition on an algebra A over a commutative ring. Our proof uses only elementary localization techniques in terms of pro-groups and stability results for K1 and K2. We also prove similar result for the Steinberg group associated with any sufficiently isotropic general linear group constructed by a quasi-finite algebra.

KW - Crossed module

KW - Isotropic linear group

KW - Steinberg group

UR - http://www.scopus.com/inward/record.url?scp=85090298285&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2020.106547

DO - 10.1016/j.jpaa.2020.106547

M3 - Article

AN - SCOPUS:85090298285

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

M1 - 106547

ER -

ID: 126321109