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arXiv · 2504.03134

Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains

George Shabat·Alexander Tumanov
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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.

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George Shabat, Alexander Tumanov. 2025-04-04. Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains. https://arxiv.org/abs/2504.03134

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