Abstract
The convolution algebra of central measures on a connected compact simple Lie group G is analyzed. It is shown that the radical of the ideal of central L 1-functions contains all continuous central measures. From this, examples of singular measures with absolutely continuous convolution square are constructed. Also, the spectrum of the algebra is determined and the continuous central measures are identified as those measures whose (central) Fourier-Stieltjes transform tends to zero at infinity in G ̂ . Finally, all the central idempotent measures are explicitly determined and it is shown that there are no infinite (central) Sidon sets in G ̂ .
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