Acta Applicandae Mathematica

, Volume 45, Issue 1, pp 73–113

Chevalley groups over commutative rings: I. Elementary calculations

  • Nikolai Vavilov
  • Eugene Plotkin

DOI: 10.1007/BF00047884

Cite this article as:
Vavilov, N. & Plotkin, E. Acta Appl Math (1996) 45: 73. doi:10.1007/BF00047884


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.

Mathematics Subject Classifications (1991)


Key words

Chevalley groups over ringselementary subgroupK1-functorWeyl modulesChevalley commutator formulaSteinberg relationsstructure constants

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Nikolai Vavilov
    • 1
    • 2
  • Eugene Plotkin
    • 3
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Department of Mathematics and MechanicsUniversity of Sant PetersburgPetrodvoretsRussia
  3. 3.Department of Mathematics and Computer ScienceBar Ilan UniversityRamat GanIsrael