论文标题
$ \ Mathrm k_2 $ - functor的中心性重新审视
Centrality of $\mathrm K_2$-functor revisited
论文作者
论文摘要
我们证明，$ \ mathrm {st}（n，a）$是$ \ mathrm {gl}（n，a）$的交叉模块。我们的证明仅根据$ \ mathrm k_1 $和$ \ mathrm k_2 $的稳定结果使用基本定位技术。我们还证明了与任何由准芬矿代数构建的足够各向同性的一般线性组相关的Steinberg组。
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.
