The yoga of commutators.

DOI10.1007/s10958-011-0617-yzbMath1318.20049arXiv1102.5414OpenAlexW1992235136MaRDI QIDQ2256708

Zuhong Zhang, Roozbeh Hazrat, Alexei Stepanov, Nikolai A. Vavilov

Publication date: 20 February 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5414

zbMATH Keywords

algebraic groupselementary subgroupsunitary groupsChevalley groupscommutator calculuscommutator widthsQuillen-Suslin lemmaelementary generatorslocalisation-completionsnilpotency of \(K_1\)nilpotent filtrations

Mathematics Subject Classification ID

Other matrix groups over rings (20H25) Commutator calculus (20F12) Other matrix groups over fields (20H20)

Related Items

Relative centralizers of relative subgroups, The commutators of classical groups, Linear groups over general rings. I: Generalities., Local-global principle for the general quadratic and general Hermitian groups and the nilpotency of \(\mathrm{KH}_1\), Word equations in simple groups and polynomial equations in simple algebras., Multiple commutator formulas., Multiple commutators of elementary subgroups: end of the line, Commutators of elementary subgroups: curiouser and curiouser, Structure of Chevalley groups over rings via universal localization., Commutators of congruence subgroups in the arithmetic case, Relative commutator calculus in Chevalley groups., Commutators of relative and unrelative elementary groups, revisited, Local-global principle for congruence subgroups of Chevalley groups., Yoga of commutators in DSER elementary orthogonal group, The yoga of commutators: further applications., Nilpotency of Odd Unitary K₁-Functor, Unrelativized standard commutator formula, Generation of relative commutator subgroups in Chevalley groups, Generation of relative commutator subgroups in Chevalley groups. II, Calculations in exceptional groups, an update., Commutators of relative and unrelative elementary unitary groups, Multiple commutator formulas for unitary groups

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