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arXiv · 2009.03999

Centrality of $\mathrm K_2$ for Chevalley groups: a pro-group approach

Andrei Lavrenov·Sergey Sinchuk·Egor Voronetsky
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Abstract

We prove the centrality of $\mathrm{K}_2 (\mathsf{F}_4, \,R)$ for an arbitrary commutative ring $R$. This completes the proof of the centrality of $\mathrm K_2(\Phi,\, R)$ for any root system $\Phi$ of rank $\geq 3$. Our proof uses only elementary localization techniques reformulated in terms of pro-groups. Another new result of the paper is the construction of a crossed module on the canonical homomorphism $\mathrm{St}(\Phi, R) \to \mathrm{G}_\mathrm{sc}(\Phi, R)$, which has not been known previouly for exceptional $\Phi$.

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Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky. 2020-09-08. Centrality of $\mathrm K_2$ for Chevalley groups: a pro-group approach. https://doi.org/10.1007/s11856-024-2608-y

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