SK1 and Lie algebras

We investigate the vanishing of the group SK 1 ( Λ ( G ) ) for the Iwasawa algebra Λ ( G ) of a pro- p p -adic Lie group G (with p ≠ 2 ). We reduce this vanishing to a linear algebra problem for Lie algebras over arbitrary rings, which we solve for Chevalley orders in split reductive Lie algebras....

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Bibliographic Details
Published in:Mathematische annalen 2013-12, Vol.357 (4), p.1455-1483
Main Authors: Schneider, Peter, Venjakob, Otmar
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:We investigate the vanishing of the group SK 1 ( Λ ( G ) ) for the Iwasawa algebra Λ ( G ) of a pro- p p -adic Lie group G (with p ≠ 2 ). We reduce this vanishing to a linear algebra problem for Lie algebras over arbitrary rings, which we solve for Chevalley orders in split reductive Lie algebras.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-013-0943-0