Entire Functions on Lie Groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918237815439360 |
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| author | Heins, Michael |
| author_facet | Heins, Michael |
| contents | Every Lie group $G$ carries a distinguished algebra of particularly well-behaved real-analytic mappings: The entire functions $\mathcal{E}(G)$. They were introduced for the purposes of strict deformation quantization. This paper establishes a one-to-one correspondence between entire functions and holomorphic mappings $\mathcal{H}(G_\mathbb{C})$ on the universal complexification $G_\mathbb{C}$ of $G$ as Fréchet algebras. Methodically, this is achieved by porting aspects of classical complex analysis into a left-invariant guise and by studying the geometry of $G_\mathbb{C}$. As a byproduct, we obtain a strict deformation quantization of the holomorphic cotangent bundle of any universal complexification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entire Functions on Lie Groups Heins, Michael Complex Variables 22E30, 30H50, 30B40 Every Lie group $G$ carries a distinguished algebra of particularly well-behaved real-analytic mappings: The entire functions $\mathcal{E}(G)$. They were introduced for the purposes of strict deformation quantization. This paper establishes a one-to-one correspondence between entire functions and holomorphic mappings $\mathcal{H}(G_\mathbb{C})$ on the universal complexification $G_\mathbb{C}$ of $G$ as Fréchet algebras. Methodically, this is achieved by porting aspects of classical complex analysis into a left-invariant guise and by studying the geometry of $G_\mathbb{C}$. As a byproduct, we obtain a strict deformation quantization of the holomorphic cotangent bundle of any universal complexification. |
| title | Entire Functions on Lie Groups |
| topic | Complex Variables 22E30, 30H50, 30B40 |
| url | https://arxiv.org/abs/2512.07479 |