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arXiv · 2004.08551

Centrality of $\mathrm K_2$-functor revisited

Egor Voronetsky
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Abstract

We prove that $\mathrm{St}(n, A)$ is a crossed module over $\mathrm{GL}(n, A)$ under a local stable rank condition on an algebra $A$ over a commutative ring. Our proof uses only elementary localization techniques in terms of pro-groups and stability results for $\mathrm K_1$ and $\mathrm K_2$. We also prove similar result for the Steinberg group associated with any sufficiently isotropic general linear group constructed by a quasi-finite algebra.

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Egor Voronetsky. 2020-04-18. Centrality of $\mathrm K_2$-functor revisited. https://doi.org/10.1016/j.jpaa.2020.106547

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