On centrality of $K_2$ for Chevalley groups of type $E_l$

Abstract

For a root system $\Phi$ of type $E_l$ and arbitrary commutative ring $R$ we show that the group $K_2(\Phi ,R)$ is contained in the centre of the Steinberg group $St(\Phi ,R)$. In course of the proof we also demonstrate an analogue of Quillen---Suslin local-global principle for $K_2(\Phi ,R)$.

References in corpus (2)

• Steinberg groups as amalgams
• Relative symplectic Steinberg group

Cited by in corpus (10)

• On centrality of even orthogonal ${\mathrm{K}}_2$
• Centrality of ${\mathrm{K}}_2$-functor revisited
• A Horrocks-type theorem for even orthogonal $K_2$
• Centrality of ${\mathrm{K}}_2$ for Chevalley groups: a pro-group approach
• Explicit presentation of relative Steinberg groups
• On the ${\mathbb{A}}^1$-invariance of ${\mathrm{K}}_2$ modeled on linear and even orthogonal groups
• Centrality of odd unitary $K_2$-functor
• On the ${\mathbb{A}}^1$-invariance of ${\mathrm{K}}_2$ of Chevalley groups of simply-laced type
• Another presentation of orthogonal Steinberg groups
• A presentation of relative unitary Steinberg groups