Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank >1 over noetherian rings

TL;DR

This paper proves that the congruence kernel is central for elementary subgroups of Chevalley groups of rank greater than one over noetherian rings, extending understanding of their algebraic structure.

Contribution

It establishes the centrality of the congruence kernel for elementary subgroups of Chevalley groups over noetherian rings, including specific cases for types C_n and G_2.

Findings

Congruence kernel is central for Chevalley groups of rank >1 over noetherian rings.

Results apply to groups of types C_n and G_2 with minor restrictions.

Enhances understanding of the algebraic structure of elementary subgroups.

Abstract

We prove the centrality of the congruence kernel for the elementary subgroup of a Chevalley group G of rank >1 over an arbitrary noetherian ring R (under some minor restrictions on R if G is of type C_n or G_2).