Abstract
Results on continuous pseudocharacters on locally compactgroups are presented and their applications to the description oftheir second continuous bounded cohomology groups areindicated. In particular, it is proved that the second realcontinuous bounded cohomology group of a connected locallycompact group is finite-dimensional.
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References
Bargmann, V.: Irreducible unitary representations of the Lorentz group, Ann. Math. 48 (1947), 568-640.
Bavard, C.: Longueur stable des commutateurs, Enseig. Math. 37 (1991), 109-150.
Besson, G.: Séminaire cohomologie bornée, Écol. Norm. Sup. Lyon, 1988.
Borel, A.: Sections locales de certains espaces fibrés, C.R. Acad. Sci. Paris 230 (1950), 1246-1248.
Bouarich, A.: Suites exactes en cohomologie bornée réelle des groups discrets, C.R. Acad. Sci. Paris 320 (1995), 1355-1359.
Feigin, B. L. and Fuchs, D. B.: Cohomologies of Lie groups and Lie algebras, in: A. L. Onishchik and E. B. Vinberg (eds), Lie Groups and Lie Algebras, II, Encyclopaedia Math. Sci. 21, Springer-Verlag, Berlin, 2000, pp. 125-223.
Gromov,M.: Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1983), 5-99.
Grosser, M.: The review of Shtern (1993), Math. Rev. 95 (1995), 22008.
Guichardet, A.: Cohomologie des groupes topologiques et des algèbres de Lie, Cedic/Fernand Nathan, Paris, 1980.
Guichardet, A. and Wigner, D.: Sur la cohomologie réele des groupes de Lie simples réels, Ann. Sci. Écol. Norm. Sup. 11 (1978), 277-292.
Hewitt, E. and Ross, K. A.: Abstract Harmonic Analysis, Vol. I, Springer-Verlag, Berlin, 1963.
Iwasawa, K.: On some types of topological groups, Ann. of Math. 50 (1949), 507-558.
Paterson, A. L. T.: Amenability, Amer. Math. Soc., Providence, RI, 1988.
Segal, G. L.: Cohomology of topological groups, in: Symposia Math. 4 (INDAM Rome, 1968/69), Academic Press, New York, 1970, pp. 377-387
Serre, J.-P.: Extensions des groupes localement compacts (mimeographed notes), Bourbaki Seminar Lecture on March 27, 1950.
Shtern, A. I.: Stability of representations and pseudocharacters, Report on Lomonosov Readings 1983, Moscow State University, Moscow, 1983.
Shtern, A. I.: Continuous pseudocharacters on connected locally compact groups are characters, Funktsional. Anal. i Prilozhen. 27(4) (1993), 94-96.
Shtern, A. I.: Quasi-symmetry. I, Russian J. Math. Phys. 2(3) (1994), 353-382.
Shtern, A. I.: Triviality and continuity of pseudocharacters and pseudorepresentations, Russian J. Math. Phys. 5(1) (1997), 135-138.
Shtern, A. I.: Bounded continuous real 2-cocycles on simply connected simple Lie groups and their applications, Russian J. Math. Phys. 8(1) (2001), 122-133.
Shtern, A. I.: Structure properties and the bounded real continuous 2-cohomology of locally compact groups, Funktsional. Anal. i Prilozhen., to appear.
Terp, C.: On locally compact groups whose set of compact subgroups is inductive, J. Lie Theory 1 (1991), 73-80.
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Shtern, A.I. Remarks on Pseudocharacters and the Real Continuous Bounded Cohomology of Connected Locally Compact Groups. Annals of Global Analysis and Geometry 20, 199–221 (2001). https://doi.org/10.1023/A:1012296430651
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DOI: https://doi.org/10.1023/A:1012296430651