A Note on Tortrat Groups

S. G. Dani and C. R. E. Raja

Journal of Theoretical Probability, 1998, vol. 11, issue 2, 571-576

Abstract: 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.

Keywords: Probability measure; connected Lie group; Tortrat group (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022600326181

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