Multiple commutators of elementary subgroups: end of the line

Nikolai Vavilov, Zuhong Zhang

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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.
Translated title of the contributionКратные коммутаторы элементарных групп: конец пути
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalLinear Algebra and Its Applications
Volume599
Early online date4 Apr 2020
DOIs
StatePublished - 15 Aug 2020

Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis
  • Algebra and Number Theory

Keywords

  • math.RA
  • General linear group
  • congruence subgroups
  • elementary subgroups
  • standard commutator formulae
  • Elementary subgroups
  • Standard commutator formulae
  • Congruence subgroups
  • GL(N,A)

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