Gelfand-Kirillov conjecture as a first-order formula
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909409319321600 |
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| author | Mariano, Hugo Luiz Schwarz, João |
| author_facet | Mariano, Hugo Luiz Schwarz, João |
| contents | Let $Σ$ be a (reduced) root system. Let $\mathsf{k}$ be an algebraically closed field of zero characteristic, and consider the corresponding semisimple Lie algebra $\mathfrak{g}_{\mathsf{k}, Σ}$. Then there is a first-order sentence $ϕ_Σ$ in the language $\mathcal{L}=(1,0,+,*,-)$ of rings such that, for any algebraically closed field $\mathsf{k}$ of characteristic 0, the validity of the Gelfand-Kirillov Conjecture for $\mathfrak{g}_{\mathsf{k}, Σ}$ is equivalent to $ACF_0 \vdash ϕ_Σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_03387 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Gelfand-Kirillov conjecture as a first-order formula Mariano, Hugo Luiz Schwarz, João Rings and Algebras Logic 2020 Primary: 03C60, Secundary: 16S85, 16W22, 17B35 Let $Σ$ be a (reduced) root system. Let $\mathsf{k}$ be an algebraically closed field of zero characteristic, and consider the corresponding semisimple Lie algebra $\mathfrak{g}_{\mathsf{k}, Σ}$. Then there is a first-order sentence $ϕ_Σ$ in the language $\mathcal{L}=(1,0,+,*,-)$ of rings such that, for any algebraically closed field $\mathsf{k}$ of characteristic 0, the validity of the Gelfand-Kirillov Conjecture for $\mathfrak{g}_{\mathsf{k}, Σ}$ is equivalent to $ACF_0 \vdash ϕ_Σ$. |
| title | Gelfand-Kirillov conjecture as a first-order formula |
| topic | Rings and Algebras Logic 2020 Primary: 03C60, Secundary: 16S85, 16W22, 17B35 |
| url | https://arxiv.org/abs/2009.03387 |