Embeddability of infinitely divisible distributions on linear Lie groups

An introduction to the embedding problem for probabilities on locally compact groups

“…Result (iii) is an easy consequence of (i) and is given as Theorem 2.1 in [6]. Result (iv) follows from (i) and Proposition 6.2 of [5].…”

“…Proof Result (i) is Theorem 3.2 of [5], and a similar argument suitably adapted gives (ii) as Theorem 2 of [22]. Result (iii) is an easy consequence of (i) and is given as Theorem 2.1 in [6].…”

“…Remarks on the proof of 4.7 (i) The theorem follows for the general case fairly simply, once it is established for the "middle case" when ρ (G) is almost algebraic (see [5,Section 7]). …”

“…In 1992, Dani and McCrudden [5] gave a proof of the embedding property for a class of Lie groups that includes all connected semisimple Lie groups and all simply-connected Lie groups. Their result is as follows.…”

“…(iii) In order to be able to deduce the middle case from the almost algebraic case, we require the added complication in the almost algebraic proof of working throughout with a subset E ⊆ P (G) which is a so called admissible root set for µ (see [5,Section 5]). But in our discussion of the reduced almost algebraic case in the next section we choose to work throughout with P (G) rather than with a general admissible root set for µ.…”