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Chevalley groups over commutative rings: I. Elementary calculations

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Abstract

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.

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  1. Fakultät für Mathematik, Universität Bielefeld, 33615, Bielefeld, Germany

    Nikolai Vavilov

  2. Department of Mathematics and Mechanics, University of Sant Petersburg, 198904, Petrodvorets, Russia

    Nikolai Vavilov

  3. Department of Mathematics and Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel

    Eugene Plotkin

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Vavilov, N., Plotkin, E. Chevalley groups over commutative rings: I. Elementary calculations. Acta Appl Math 45, 73–113 (1996). https://doi.org/10.1007/BF00047884

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