Constructs Steinberg group functors for locally isotropic reductive groups over rings and proves centrality of the K2-functor.
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6 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 6representative citing papers
Groups with BC_ℓ root subgroups obeying natural commutator relations are homomorphic images of odd unitary Steinberg groups over odd form rings with Peirce decompositions.
Steinberg pro-groups for GL, odd unitary, and Chevalley groups satisfy the Zariski cosheaf property as crossed pro-modules, with an analogue of commutator formulas and an action of base groups over localized rings.
Explicit presentations are given for relative Steinberg groups of types Bℓ, Cℓ, F4 (ℓ≥3) and odd unitary Steinberg groups over the specified rings.
StO(M, q) admits van der Kallen's another presentation via the pro-group approach when q is sufficiently isotropic.
Constructs twisted forms of classical reductive group schemes from augmented odd form algebras and shows classical isotropic reductive groups are odd unitary groups up to isogeny, excluding small-rank cases.
citing papers explorer
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Locally isotropic Steinberg groups I. Centrality of the $\mathrm K_2$-functor
Constructs Steinberg group functors for locally isotropic reductive groups over rings and proves centrality of the K2-functor.
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Groups with $\mathsf{BC}_\ell$-commutator relations
Groups with BC_ℓ root subgroups obeying natural commutator relations are homomorphic images of odd unitary Steinberg groups over odd form rings with Peirce decompositions.
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Cosheaves of Steinberg pro-groups
Steinberg pro-groups for GL, odd unitary, and Chevalley groups satisfy the Zariski cosheaf property as crossed pro-modules, with an analogue of commutator formulas and an action of base groups over localized rings.
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A presentation of relative unitary Steinberg groups
Explicit presentations are given for relative Steinberg groups of types Bℓ, Cℓ, F4 (ℓ≥3) and odd unitary Steinberg groups over the specified rings.
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Another presentation of orthogonal Steinberg groups
StO(M, q) admits van der Kallen's another presentation via the pro-group approach when q is sufficiently isotropic.
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Twisted forms of classical groups
Constructs twisted forms of classical reductive group schemes from augmented odd form algebras and shows classical isotropic reductive groups are odd unitary groups up to isogeny, excluding small-rank cases.