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

TL;DR

This paper explores which non-linear Lie groups can be realized as automorphism groups of bounded complex domains, extending previous results that focused on linear Lie groups, and provides new examples of such groups.

Contribution

It extends the classification of Lie groups realizable as automorphism groups of bounded domains to include certain non-linear groups, building on earlier work with linear groups.

Findings

Identifies non-linear Lie groups that can be automorphism groups of bounded domains

Provides explicit examples of such non-linear groups

Extends the scope of known realizable Lie groups in complex analysis

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.