In the present thesis we study the rigidity phenomenon in the Kac-Moody context.One can realize split Kac-Moody groups as canonical infinite dimensional generalizations of Chevalley groups. There exists rich literature for the rigidity of arithmetic Chevalley groups. This thesis benefits significantly from the rigidity of arithmetic Chevalley groups.Our goal is to obtain similar rigidity results for arithmetic Kac-Moody group as there exist for arithmetic Chevalley groups. Namely, we prove the super rigidity and the strong rigidity for certain split Kac-Moody groups.In order to achieve our goals first we localize the arguments to semisimple bounded subgroups of split Kac-Moody groups which can be realized as Chevalley groups. This is achieved by applying building theory in the Kac-Moody context. Then by means of the rigidity results for arithmetic Chevalley groups, we obtain local rigidity for split Kac-Moody groups.An important feature of certain split Kac-Moody groups is their universality on their rank one and rank two fundamental subgroups. Hence, by means of local to global arguments we obtain global rigidity results for arithmetic Kac-Moody groups.
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