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arxiv: 2310.01592 · v2 · submitted 2023-10-02 · 🧮 math.GR

Locally isotropic elementary groups

Egor Voronetsky This is my paper
classification 🧮 math.GR
keywords groupselementaryisotropicrankringsappliedautomorphismbasic
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We construct elementary subgroups of all reductive groups of the local isotropic rank $\geq 2$ over rings and prove their basic properties. In particular, our results may be applied to the automorphism groups of any finitely generated projective modules over commutative unital rings of rank $\geq 3$ at every prime ideal.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Locally isotropic Steinberg groups II. Schur multipliers

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    Computes Schur multipliers for locally isotropic Steinberg groups and root graded Steinberg groups of rank at least 3 (excluding H3 and H4), proving the former are well-defined as abstract groups.

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    math.RT 2026-01 unverdicted novelty 5.0

    An explicit formula is given for squares of Weyl elements in isotropic reductive groups over commutative rings, with classification in rank one groups.