具有多项式系数的简单向量李超代数的极大分次子代数
Maximal graded subalgebras of simple vectorial Lie superalgebras with polynomial coefficients
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中文总结 AI 辅助
本文研究了具有多项式系数的简单向量李超代数在 Weisfeiler 滤过分次下的极大简单分次子代数，结合矩阵情形解决了 Dynkin 问题的超与无限维版本。
中文摘要 AI 辅助
S. Lie 是第一个尝试对具有多项式系数的简单向量（即由向量场组成的）李代数的极大子代数进行分类的人。在附录中表明，如所述，该问题是野性的：描述所有子代数包含了对矩阵对在同时共轭下的分类，因此这样的子代数过多。多位研究者区分了在应用中重要的各类极大子代数。在此，对于具有多项式系数的简单（或接近简单的 Cartan 延拓）向量李超代数，考虑与 Weisfeiler 滤过相关的分次，我们描述了极大简单（及接近简单）的分次子代数——这是 Sophus Lie 所处理问题的超化版本。结合 I. Shchepochkina 对矩阵李超代数的极大子代数的描述（见 arXiv:hep-th/9702122），本文解决了 Dynkin 问题的超和无限维版本——即描述简单有限维李代数的极大子代数——除了在别处处理的 3 个例外环境。
英文摘要
S. Lie was the first to try to classify maximal subalgebras of simple vectorial (i.e., consisting of vector fields) Lie algebras with polynomial coefficients. In Appendix it is shown that, as stated, the problem is wild: describing all subalgebras contains the classification of pairs of matrices up to simultaneous conjugation, so there are too many such subalgebras. Several researchers distinguished various classes of maximal subalgebras important in applications. Here, in simple (or in Cartan prolongations close to simple) vectorial Lie superalgebras with polynomial coefficients considered with gradings associated with Weisfeiler filtrations, we describe maximal simple (and close to simple) graded subalgebras --- a superization of what Sophus Lie tackled. Together with I. Shchepochkina's description of the maximal subalgebras of matrix Lie superalgebras, see arXiv:hep-th/9702122, this paper solves the super and infinite-dimensional version of Dynkin's problem --- the description of the maximal subalgebras of simple finite-dimensional Lie algebras --- except for the 3 exceptional ambients considered elsewhere.
发表机构
- Stockholm University（斯德哥尔摩大学）
- Independent University of Moscow（莫斯科独立大学）
机构由 AI 辅助整理，请以论文原文为准。
