We describe certain sufficient conditions for an infinitely divisible
probability measure on a class of connected Lie groups to be embeddable in a
continuous one-parameter convolution semigroup of probability measures.
(Theorem 1.3). This enables us in particular to conclude the embeddability of
all infinitely divisible probability measures on certain Lie groups, including
the so called Walnut group (Corollary 1.5). The embeddability is concluded also
under certain other conditions (Corollary 1.4 and Theorem 1.6).Comment: 24 page
