Triangular systems of probability measures on simply connected nilpotent and discrete subgroups of exponential Lie groups

Abstract

For simply connected nilpotent Lie groups G, we show that limit laws of infinitesimal triangular systems Δ of symmetric probability measures on G are infinitely divisible even if Δ is not commutative. The same holds also if the measures of Δ are supported by some fixed discrete subgroup Γ⊂G. Furthermore, we give a weakening of Wehn's conditions for the accompanying laws theorem in the case of discrete subgroups of exponential Lie groups.