## Central idempotent measures on compact groups

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- by Daniel Rider PDF
- Trans. Amer. Math. Soc.
**186**(1973), 459-479 Request permission

## Abstract:

Let*G*be a compact group with dual object $\Gamma = \Gamma (G)$ and let $M(G)$ be the convolution algebra of regular finite Borel measures on

*G*. The author has characterized the central idempotent measures on certain

*G*, including the unitary groups, in terms of the hypercoset structure of $\Gamma$. The characterization also says that, on certain

*G*, a central idempotent measure is a sum of such measures each of which is absolutely continuous with respect to the Haar measure of a closed normal subgroup. The main result of this paper is an extension of this characterization to products of certain groups. The known structure of connected groups and a recent result of Ragozin on connected simple Lie groups will then show that the characterization is valid for connected groups. On the other hand, a simple example will show it is false in general for non-connected groups. This characterization was done by Cohen for abelian groups and the proof borrows extensively from Amemiya and Itô’s simplified proof of Cohen’s result.

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## Additional Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**186**(1973), 459-479 - MSC: Primary 43A05; Secondary 22C05
- DOI: https://doi.org/10.1090/S0002-9947-1973-0340961-0
- MathSciNet review: 0340961