Centrality of $\mathrm K_2$-functor revisited

Egor Voronetsky

doi:10.1016/j.jpaa.2020.106547

paper

Centrality of $K_{2}$ -functor revisited

arXiv:2004.08551 · doi:10.1016/j.jpaa.2020.106547

Abstract

We prove that $St (n, A)$ is a crossed module over $GL (n, A)$ 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 $K_{1}$ and $K_{2}$ . We also prove similar result for the Steinberg group associated with any sufficiently isotropic general linear group constructed by a quasi-finite algebra.

I corrected the statement of proposition 3 and some minor misprints

Centrality of K2​-functor revisited

Abstract

Centrality of $K_{2}$ -functor revisited