Universal laws on simply connected step 2-nilpotent Lie groups
Let \(G\) be a simply connected 2-step nilpotent Lie group, in particular the Heisenberg group, and \({\mathcal G}\) its Lie algebra. Each object \(\Xi\) on \(G\) can be identified with the corresponding object \(^0 \Xi\) on \({\mathcal G}\). The author proves the following analogue of Remark 3.4 of \textit{W. Hazod}'s paper [Ann. Inst. Henri Poincaré, Probab. Stat. 29, No. 3, 339-355 (1993; Zbl 0812.60013)]. Theorem. Let \(A \in \Aut(G)\). Then a probability measure \(\nu \in {\mathcal M}^1 (G)\) is \(A\)-universal if and only if \(^0 \nu\) is \(A\)-universal on \({\mathcal G}\).
scientific article; zbMATH DE number 857528