Structure of Chevalley groups over rings via universal localization

Chevalley Groups over Commutative Rings

Chevalley Groups over Commutative Rings I. Elementary Calculations

This is the rst 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 result...

Chow Rings and Cobordism of Some Chevalley Groups

We compute the cobordism rings of the classifying spaces of a certain class of Chevalley groups. In the particular case of the general linear group, we prove that it is isomorphic to the Chow ring.

Infinite Dimensional Chevalley Groups and Kac-moody Groups over Z

Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is given by five axioms KMG1-KMG5 which are natural extensions of the properties of Chevalley-Demazure group schemes. We give a construction of the Tits functor for symmetrizable Kac-Moody groups G using i...

Non-zero Ext for Chevalley Groups (via Algebraic Groups)

Take G to be a split, simply-connected semisimple algebraic group (for example, SL(w, K) or Sp(2m, K)) over an algebraic closure K of the field of p elements, where p is prime. Denote by G(n) the finite subgroup consisting of elements of G defined over the field of p elements. The simple (rational) G-modules L(X) are parametrized by the set X of dominant weights, a subset of the character group...