Journal of Lie Theory

no. 2
Reduced 1-Cohomology of Connected Locally Compact Groups and Applications
Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 311-328
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.
DOI: 10.5802/jolt.412
Classification: 22D10, 22E30, 22A05
Keywords: Cohomology, unitary representation, locally compact group 
@article{JOLT_2006_16_2_a6,
     author = {F. Martin},
     title = {Reduced {1-Cohomology} of {Connected} {Locally} {Compact} {Groups} and {Applications}},
     journal = {Journal of Lie Theory},
     pages = {311--328},
     year = {2006},
     volume = {16},
     number = {2},
     doi = {10.5802/jolt.412},
     zbl = {1115.22006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.412/}
}
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F. Martin. Reduced 1-Cohomology of Connected Locally Compact Groups and Applications. Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 311-328. doi: 10.5802/jolt.412

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