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Journal of Lie Theory 16 (2006), No. 2, 311--328
Copyright Heldermann Verlag 2006

Reduced 1-Cohomology of Connected Locally Compact Groups and Applications

Florian Martin
Philip Morris Int'l R&D, Quais Jeanrenaud 56, 2003 Neuchâtel, Switzerland

We focus on the reduced 1-cohomology spaces of locally compact connected groups with coefficients in unitary representations. The vanishing of these spaces for every unitary irreducible representation characterizes Kazhdan's property (T). The main theorem states that for a connected locally compact group, there are only a finite number of unitary irreducible representations for which the reduced 1-cohomology does not vanish. Moreover, a description of these representations is given.

Keywords: Cohomology, unitary representation, locally compact group.

MSC: 22D10, 22E30, 22A05

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