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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: S. P. Wang
Journal: Proc. Amer. Math. Soc. 42 (1974), 621-624
MSC: Primary 22E40
MathSciNet review: 0354936
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0354936-5
PII: S 0002-9939(1974)0354936-5
Keywords: Locally compact groups, groups with property (T), affine semisimple algebraic groups
Article copyright: © Copyright 1974 American Mathematical Society