| 姚裕丰.限制Hamiltonian型及Contact型李代数的不可约表示[J].数学年刊A辑,2012,33(4):483~496 |
| 限制Hamiltonian型及Contact型李代数的不可约表示 |
| Irreducible Representations of Restricted Lie Algebras of Hamiltonian Type and Contact Type |
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| DOI： |
| 中文关键词: Cartan型李代数 Hamiltonian型李代数 Contact型李代数 广义限制李代数 广义x-约化表示 |
| 英文关键词:Cartan type Lie algebra, Lie algebra of Hamiltonian type, Lie algebra
of contact type, Generalized restricted Lie algebra, Generalized
-reduced representation |
| 基金项目:国家自然科学基金(No.11126062)资助的项目 |
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| 中文摘要: |
| 设L=H（2r;1）或K（2r+1;1）是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约Uχ（L）-模都是从不可约Uχ(L[O].I)-模诱导的. |
| 英文摘要: |
| Let $L=H(2r;\textbf{1})$ or $K(2r+1;\textbf{1})$ be a restricted Lie algebra of
Hamiltonian type or contact type over an algebraically closed field $F$ of characteristic $p>2$.
Based on the study of irreducible representations of generalized Jacobson-Witt algebras and
special algebras, with the aid of the gradation structure of $L$: $L=\bigoplus\limits_{q\in\bbz}L_{[q],I}$,
where $I$ is a subset of $\{1,2,\cdots,r\}$, it is proved that when the $p$-characteristic function
$\chi$ is regular semisimple, each simple $U_{\chi}(L)$-module
is induced from a simple $U_{\chi}(L_{[0],I})$-module. |
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