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Zap. Nauchn. Sem. POMI, 2018, Volume 470, Pages 38–49 (Mi znsl6610)  

Unrelativised standard commutator formula

N. Vavilov

St. Petersburg State University

Abstract: In the present note, which is a marginalia to the previous papers by Roozbeh Hazrat, Alexei Stepanov, Zuhong Zhang, and the author, I observe that for any ideals $A,B\unlhd R$ of a commutative ring $R$ and all $n\ge3$ the birelative standard commutator formula also holds in the unrelativised form, as $[E(n,A),\mathrm{GL}(n,B)]=[E(n,A),E(n,B)]$ and discuss some obvious corollaries thereof.

Key words and phrases: general linear group, congruence subgroups, elementary subgroups, standard commutator formulae.

Funding Agency Grant Number
Russian Science Foundation 17-11-01261
This publication is supported by Russian Science Foundation grant 17-11-01261.


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Document Type: Article
UDC: 512.5
Received: 23.10.2018
Language: English

Citation: N. Vavilov, “Unrelativised standard commutator formula”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 38–49

Citation in format AMSBIB
\Bibitem{Vav18}
\by N.~Vavilov
\paper Unrelativised standard commutator formula
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 38--49
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6610}


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