Centrality of odd unitary K₂-functor

2020/05/06 by Voronetsky, Egor
#19C09 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2005.02926

Abstract

Let (R, Δ) be an odd form algebra. We show that the unitary Steinberg group StU(R, Δ) is a crossed module over the odd unitary group \mathrm U(R, Δ) in two major cases: if the odd form algebra has a free orthogonal hyperbolic family satisfying a local stable rank condition and if the odd form algebra is sufficiently isotropic and quasi-finite. The proof uses only elementary localization techniques in terms of pro-groups.

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