Centrality of odd unitary $K_2$-functor
2020
Let $(R, \Delta)$ be an odd form algebra. We show that the unitary Steinberg group $\mathrm{StU}(R, \Delta)$ is a crossed module over the odd unitary group $\mathrm U(R, \Delta)$ 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 and stability results for $\mathrm{KU}_1$ and $\mathrm{KU}_2$.
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