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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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