Central measures on semisimple Lie groups have essentially compact support
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- by David L. Ragozin and Linda Preiss Rothschild PDF
- Proc. Amer. Math. Soc. 32 (1972), 585-589 Request permission
Abstract:
In this paper it is shown that for a connected semisimple Lie group with no nontrivial compact quotient any finite central measure is a discrete measure concentrated on the center of the group. More generally, the largest possible support set for a central measure on any semisimple Lie group is determined. From these results it follows that the center of the algebra ${L_1}(H)$ is trivial for any locally compact group H which has a noncompact connected simple Lie group as a homomorphic image.References
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496 —, Abstract harmonic analysis. Vol. 2: Structure and analysis for compact groups, analysis on locally compact Abelian groups, Die Grundlehren der math. Wissenschaften, Band 152, Springer-Verlag, New York, 1970. MR 41 #7378.
- Richard D. Mosak, Central functions in group algebras, Proc. Amer. Math. Soc. 29 (1971), 613–616. MR 279602, DOI 10.1090/S0002-9939-1971-0279602-3
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 585-589
- MSC: Primary 43A05; Secondary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291373-4
- MathSciNet review: 0291373