Simple superelliptic Lie algebras
Simple superelliptic Lie algebras
复制标题
简单超椭圆李代数
DOI：
10.1142/s0219199716500322
复制
发表时间：
2017
影响因子：
1.6
通讯作者：
Zhao Kaiming
中科院分区：
文献类型：
--
作者：
Cox Ben;Guo Xiangqian;Lu Rencai;Zhao Kaiming
设$m\in N$，$P（t）\in C[t]$。然后我们有黎曼曲面（交换代数）$R_m（P）=C[t^{\pm1}，u| u^m=P（t）]$和$S_m（P）=C[t，u| u^m=P（t）].$李代数$\mathcal{R}_m（P）=Der（R_m（P））$和$\mathcal{S}_m（P）=Der（S_m（P））$称为$m$阶超椭圆李代数。本文给出了这类李代数为单李代数的充要条件，并确定了它们的泛中心扩张和导子代数。我们还研究了这些李代数的同构和自同构问题。
Let $m\in N$, $P(t)\in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{\pm1},u | u^m=P(t)]$ and $S_m(P)=C[t , u| u^m=P(t)].$ The Lie algebras $\mathcal{R}_m(P)=Der(R_m(P))$ and $\mathcal{S}_m(P)=Der(S_m(P))$ are called the $m$-th superelliptic Lie algebras associated to $P(t)$. In this paper we determine the necessary and sufficient conditions for such Lie algebras to be simple, and determine their universal central extensions and their derivation algebras. We also study the isomorphism and automorphism problem for these Lie algebras.