On the first cohomology group of discrete groups with property (𝑇)

Wang, S. P.

doi:10.1090/S0002-9939-1974-0354936-5

On the first cohomology group of discrete groups with property $(T)$
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Proc. Amer. Math. Soc. 42 (1974), 621-624 Request permission

Abstract:

Let G be a separable locally compact group with property (T), i.e., the class of one dimensional trivial representations is an isolated point in the dual space Ĝ of G. Let $\pi :G \to {O_n}$ be a continuous representation of G into the orthogonal group. In this note, we show that ${H^1}(G,\pi ) = 0$.

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