Non-linear Lie groups that can be realized as automorphism groups of bounded domains

Abstract

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in ${\mathbb C}^n$. In an earlier paper of 1990, we proved the result for connected linear Lie groups. In this paper we give examples of non-linear groups for which the result still holds.