arXiv · 1606.00272
We give a short uniform proof of centrality of $\mathrm K_2(\Phi,\,R)$ for all simply-laced root systems $\Phi$ of rank $\geq3$.
Andrei Lavrenov, Sergey Sinchuk. 2016-06-01. On centrality of even orthogonal $\mathrm K_2$. https://doi.org/10.1016/j.jpaa.2016.09.004
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The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative complex Banach algebra. In his 1974 ICM address, Taylor asked whether the higher cohomology groups admit descriptions in terms of the underlying ring. We give a solution to this question in even degrees: The \'etale (aka Lichtenbaum) Chow group in every codimension is canonically isomorphic to the corresponding even integral cohomology group of the Gelfand spectrum.
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