论文标题
Gelfand-Kirillov猜想是一阶公式
Gelfand-Kirillov conjecture as a first-order formula
论文作者
论文摘要
令$σ$为（简化）根系。令$ \ mathsf {k} $为零特征的代数封闭字段，并考虑相应的semimple lie代数$ \ mathfrak {g} _ {\ mathsf {k}，σ} $。然后，语言中有一个一阶句子$ \ mathcal {l} =（1,0，+，*， - ）$的$，以至于对于特征性0的任何代数封闭的字段$ \ mathsf {k} $ 0 σ} $相当于$ acf_0 \ vdash ϕ_σ $。
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 $ACF_0 \vdash ϕ_Σ$.
