再论$\mathrm K_2$ -函子的中心性
Centrality of $\mathrm K_2$-functor revisited
摘要：
证明了交换环上的代数$A$在局部稳定秩条件下，$\mathrm{St}(n, A)$是$\mathrm{GL}(n, A)$上的交叉模.我们的证明只使用基本的本地化技术的亲组和稳定性结果$\mathrm K_1$和$\mathrm K_2$。对于由拟有限代数构造的充分迷向一般线性群所对应的Steinberg群，我们也证明了类似的结果.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
