Simplicity of Some Twin Tree Automorphism Groups with Trivial Commutation Relations. Issue 2 (14th June 2014)

• Record Type: Journal Article
• Authors: Morita, Jun; Rémy, Bertrand
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 2(2014)
• Page Start: 390
• Page End: 400
• Publication Date: 2014-06-14
• Subjects: 20G44 -- 20E42 -- 51E24; Kac–Moody group -- twin tree -- simplicity -- root system -- building; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2014-002-2
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: We prove simplicity for incomplete rank 2 Kac—Moody groups over algebraic closures of finite fields with trivial commutation relations between root groups corresponding to prenilpotent pairs. We don't use the (yet unknown) simplicity of the corresponding finitely generated groups ( i.e., when the ground field is finite). Nevertheless we use the fact that the latter groups are just infinite (modulo center).