K1 of Chevalley groups are nilpotent


Autoria(s): Hazrat, Roozbeh; Vavilov, N.
Data(s)

01/04/2003

Resumo

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Identificador

http://pure.qub.ac.uk/portal/en/publications/k1-of-chevalley-groups-are-nilpotent(6911f460-674d-4a28-876b-8472dda22d55).html

http://dx.doi.org/10.1016/S0022-4049(02)00292-X

http://www.scopus.com/inward/record.url?scp=0037398185&partnerID=8YFLogxK

Idioma(s)

eng

Direitos

info:eu-repo/semantics/restrictedAccess

Fonte

Hazrat , R & Vavilov , N 2003 , ' K1 of Chevalley groups are nilpotent ' Journal of Pure and Applied Algebra , vol 179(1-2) , no. 1-2 , pp. 99-116 . DOI: 10.1016/S0022-4049(02)00292-X

Palavras-Chave #/dk/atira/pure/subjectarea/asjc/2600/2602 #Algebra and Number Theory
Tipo

article