Abstract
A locally compact group G is called a Tortrat group if for any probability measure λ on G which is not idempotent, the closure of {gλg −1 | g∈G} does not contain any idempotent measure. We show that a connected Lie group G is a Tortrat group if and only if for all g∈G all eigenvalues of Ad g are of absolute value 1. Together with well-known results this also implies that a connected locally compact group is a Tortrat group if and only if it is of polynomial growth.
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Dani, S.G., Raja, C.R.E. A Note on Tortrat Groups. Journal of Theoretical Probability 11, 571–576 (1998). https://doi.org/10.1023/A:1022600326181
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DOI: https://doi.org/10.1023/A:1022600326181