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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Central measures on semisimple Lie groups have essentially compact support

Authors: David L. Ragozin and Linda Preiss Rothschild
Journal: Proc. Amer. Math. Soc. 32 (1972), 585-589
MSC: Primary 43A05; Secondary 22E30
MathSciNet review: 0291373
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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.

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Keywords: Central measures, measures on Lie groups
Article copyright: © Copyright 1972 American Mathematical Society