Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains
Complex Variables
2025-04-07 v1
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 the affine complex space. In an earlier paper of 1990, we proved the result for connected linear Lie groups. In this paper we prove the result for a fairly large class of Lie groups including all connected real semisimple groups. This class contains many non-linear Lie groups.
Cite
@article{arxiv.2504.03134,
title = {Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains},
author = {George Shabat and Alexander Tumanov},
journal= {arXiv preprint arXiv:2504.03134},
year = {2025}
}
Comments
13 pages