Relative unitary commutator calculus, and applications

Roozbeh Hazrat*, Nikolai Vavilov, Zuhong Zhang

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

19 引用 (Scopus)

摘要

This note revisits localisation and patching method in the setting of generalised unitary groups. Introducing certain subgroups of relative elementary unitary groups, we develop relative versions of the conjugation calculus and the commutator calculus in unitary groups, which are both more general, and substantially easier than the ones available in the literature. For the general linear group such relative commutator calculus has been recently developed by the first and the third authors. As an application we prove the mixed commutator formula,. [EU(2n,I,Γ),GU(2n,J,Δ)]=[EU(2n,I,Γ),EU(2n,J,Δ)], for two form ideals (I,Γ) and (J,Δ) of a form ring (A,Λ). This answers two problems posed in a paper by Alexei Stepanov and the second author.

源语言英语
页(从-至)107-137
页数31
期刊Journal of Algebra
343
1
DOI
出版状态已出版 - 1 10月 2011

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