0. Introduction. Let G be a Chevalley-Demazure group scheme associated with a connected complex semi-simple Lie group Gc (as for the definition, see E. Abe [1], 1) and let R be a commutative ring with a unit, α an ideal of R. Then the natural ring homomorphism f:R—+R/a induces the group homomorphism (?(/): G{R) —• G(R/a). The kernel (resp. the inverse image of the center of G(R/a)) of G(f) will be denoted by G(R, α) (resp. G*(R, α)) and called the special (resp. general) congruence subgroup modulo α of G(R). Any subgroup N of G{R) such that

https://projecteuclid.org/download/pdf_1/euclid.tmj/1178240833

On normal subgroups of chevalley groups over commutative rings

This is the first in a series of papers dedicated to the structure of Chevalley groups over commutative rings. The goal of this series is to systematically develop methods of calculations in Chevalley groups over rings, based on the use of their minimal modules. As an application, we give new direct proofs for normality of the elementary subgroup, description of normal subgroups and similar results due to E. Abe, G. Taddei, L. N. Vaserstein, and others, as well as some generalizations. In this first part we outline the whole project, reproduce construction of Chevalley groups and their elementary subgroups, recall familiar facts about the elementary calculations in these groups, and fix a specific choice of the structure constants.

/pdf/chevalley-groups-over-commutative-rings-i-elementary-sn9h53yec5.pdf

Chevalley groups over commutative rings: I. Elementary calculations

Decomposition of Transvections: A Theme with Variations

K1 of Chevalley groups are nilpotent

This is the first in a series of papers dedicated to the structure of hyperbolic unitary groups over form rings and their subgroups. In this part, we recall foundations of the theory and study the elementary subgroup of the hyperbolic unitary group over a form ring. In particular, using a variant of Suslin’s patching method, we prove standard commutator formulae for relative elementary subgroups.

/pdf/structure-of-hyperbolic-unitary-groups-i-elementary-4alirlr1b3.pdf

Structure of hyperbolic unitary groups i. elementary subgroups

/pdf/chevalley-groups-over-local-rings-2q726kzsxf.pdf

Eiichi Abe

Papers

On normal subgroups of chevalley groups over commutative rings

Chevalley groups over local rings