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We construct certain Steinberg groups associated to extended aï¬ne Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended aï¬ne Lie algebra. Afterwards, we show that the extended aï¬ne Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to KacâMoody groups.
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