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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.

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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}
}

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13 pages