AI 中文总结
本文采用组合方法，研究Verlinde范畴中带典范基本群作用的单Lie代数，给出长度至多为3或作为单代数群Lie代数沿主态射限制之子代数的详尽列表，解答了相关问题与猜想。
AI 中文摘要
本文研究Verlinde范畴中带有典范基本群作用的单Lie代数，采用组合方法。我们给出了这类Lie代数的详尽列表，它们要么长度至多为3，要么作为单代数群的Lie代数沿主态射限制的子代数出现。所得结果及例外情形解答了关于代数群及其Lie代数的Verlinde范畴的若干问题与猜想。
英文摘要
This paper studies simple Lie algebras in the Verlinde category, with canonical fundamental group action, using combinatorial methods. We give an exhaustive list of such Lie algebras which either have length at most 3, or appear as a subalgebra of the restriction of the Lie algebra of a simple algebraic group along a principal morphism. The results and exceptions answer several questions and conjectures regarding Verlinde categories of algebraic groups and their Lie algebras.
Comments32 pages
