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Reduced 1-Cohomology of Connected Locally Compact Groups and Applications
Journal of Lie theory, Tome 16 (2006) no. 2, pp. 311-328 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 22D10, 22E30, 22A05
Mots-clés : Cohomology, unitary representation, locally compact group 
@article{JLT_2006_16_2_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_2_JLT_2006_16_2_a6/}
}
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F. Martin . Reduced 1-Cohomology of Connected Locally Compact Groups and Applications. Journal of Lie theory, Tome 16 (2006) no. 2, pp. 311-328. http://geodesic.mathdoc.fr/item/JLT_2006_16_2_JLT_2006_16_2_a6/