Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912309137375232 |
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| author | Shabat, George Tumanov, Alexander |
| author_facet | Shabat, George Tumanov, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains Shabat, George Tumanov, Alexander Complex Variables 32M18, 22F50 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. |
| title | Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains |
| topic | Complex Variables 32M18, 22F50 |
| url | https://arxiv.org/abs/2504.03134 |