What type of study is this?

This is a Quantitative Study study.

October 16, 2025Open Access

Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains

Key Points

The research confirms that a wide class of lie groups can be represented as automorphism groups.
The focus is on all connected real semisimple groups, broadening previous results for linear lie groups.
The results expand the understanding of interactions between complex geometry and lie group theory.
These findings may offer new avenues for research in the structure of non-linear lie groups.

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.

Read Full Paperexternally

Ask AI

Helpful

Bookmark

View Full Paper

Cite This Study

Shabat et al. (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fcfbf https://doi.org/https://doi.org/10.48550/arxiv.2504.03134

Ask AI

Helpful

Bookmark

View Full Paper