Bergman中心化定理与量子化
Bergman's Centralizer Theorem and quantization
摘要：
利用广义矩阵和Kontsevich的量子化方法证明了Bergman关于中心化子的定理。对任意正特征域$\textbf{k} $，设$A=\textbf{k} \langle x_1,\dots,x_s\rangle$是自由结合代数，则任意非平凡元$f\in A\backslash \textbf{k}$的中心化子$\mathcal{C}(f)$是单变量多项式环.证明了$A$不存在超越度为$\geq 2$的交换子代数.
英文摘要：
We prove Bergman's theorem on centralizers by using generic matrices and Kontsevich's quantization method. For any field $\textbf{k} $ of positive characteristics, set $A=\textbf{k} \langle x_1,\dots,x_s\rangle$ be a free associative algebra, then any centralizer $\mathcal{C}(f)$ of nontrivial element $f\in A\backslash \textbf{k}$ is a ring of polynomials on a single variable. We also prove that there is no commutative subalgebra with transcendent degree $\geq 2$ of $A$.
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