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Simplicity of Some Twin Tree Automorphism Groups with Trivial Commutation Relations

Published online by Cambridge University Press:  20 November 2018

Jun Morita  and
Bertrand Rémy
Jun Morita
Affiliation:
Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan e-mail: morita@math.tsukuba.ac.jp
Bertrand Rémy
Affiliation:
Université Lyon 1, Institut Camille Jordan, UMR 5208 du CNRS, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France e-mail: remy@math.univ-lyon1.fr
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Abstract

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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).

Keywords

20G4420E4251E24Kac–Moody grouptwin treesimplicityroot systembuilding
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 390 - 400
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

The first author was supported in part by Grant-in-aid for Science Research (Monkasho Kakenhi) in Japan. The second author was supported in part by the Institut Universitaire de France.

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