caa a22 4500 477076912 CHVBK 20180405111440.0 cr unu---uuuuu 170330e19961001xx s 000 0 eng 10.1007/BF00047884 doi (NATIONALLICENCE)springer-10.1007/BF00047884 Chevalley groups over commutative rings: I. Elementary calculations [Elektronische Daten] [Nikolai Vavilov, Eugene Plotkin] 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. Kluwer Academic Publishers, 1996 Chevalley groups over rings nationallicence elementary subgroup nationallicence K 1-functor nationallicence Weyl modules nationallicence Chevalley commutator formula nationallicence Steinberg relations nationallicence structure constants nationallicence Vavilov Nikolai Fakultät für Mathematik, Universität Bielefeld, 33615, Bielefeld, Germany aut Plotkin Eugene Department of Mathematics and Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel aut Acta Applicandae Mathematica Kluwer Academic Publishers 45/1(1996-10-01), 73-113 0167-8019 45:1<73 1996 45 10440 https://doi.org/10.1007/BF00047884 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00047884 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vavilov Nikolai Fakultät für Mathematik, Universität Bielefeld, 33615, Bielefeld, Germany aut NATIONALLICENCE 700 1- Plotkin Eugene Department of Mathematics and Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 45/1(1996-10-01), 73-113 0167-8019 45:1<73 1996 45 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer