Abstract: | A locally compact group G is called a Tortrat group if for any probability measure on G which is not idempotent, the closure of {g g
–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. |