Affinely infinitely divisible distributions and the embedding problem (Q5896767)

In [Math. Res. Lett. 9, 607--620 (2002; Zbl 1028.43001)] the authors proved the following theorem: Every affinely infinitely divisible probability measure on a connected abelian Lie group \(A\) is infinitely divisible on \(A\). They proved the theorem by using a result from \textit{S. G. Dani, M. McCrudden} and \textit{S. Walker} [Math. Z. 245, 781--790 (2003; Zbl 1050.22009)] on the embeddability of infinitely divisible probability measures on a class of Lie groups with compact (nontrivial) center. It turned out that the proof of the result in the latter paper has an error (see [``Erratum to our paper `On the embedding problem for infinitely divisible distributions on certain Lie groups with total center''', to appear] for details). In this paper, the authors show that the proof of the theorem in [\textit{S. G. Dani} and \textit{K. Schmidt} (op. cit.)] can be completed without recourse to the result from [\textit{S. G. Dani, M. McCrudden} and \textit{S. Walker} (op. cit.)].