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

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C Superscript n"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {C}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . In an earlier paper of 1990, we proved the result for connected <italic>linear</italic> Lie groups. In this paper we give examples of non-linear groups for which the result still holds.