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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Conceptual explanation for failure of Kazhdan's property (T) for most rank 1 groups

Kazhdan himself proved in his 1967 paper (where he introduced property (T)) that simple Lie groups $G$ of real rank $\textrm{rk}_{\mathbf{R}}(G) \geq 2$ have the property (T). This fact can be proven …
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