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Journal of Lie Theory 26 (2016), No. 4, 1079--1105
Copyright Heldermann Verlag 2016

Isomorphisms and Rigidity of Arithmetic Kac-Moody Groups

Amir Farahmand Parsa
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Max Horn
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Ralf Kцhl
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

We solve the isomorphism problem for subgroups of integral points of two-spherical Kac-Moody groups over the rational numbers. Along the way we establish versions of Mostow-Margulis strong rigidity and Margulis superrigidity with target in two-spherical split Kac-Moody groups over the rational numbers for arithmetically defined subgroups.

Keywords: Arithmetic Kac-Moody group, twin building, isomorphism problem, Mostow-Margulis strong rigidity, Margulis superrigidity.

MSC: 20G44, 20G25, 51E24

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