The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a “meander”: a planar graph associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context.

李代数的指数是一个重要的代数不变量，但众所周知它很难计算。然而，对于暗示性命名的海藻代数，索引的计算可以简化为基于“曲流”的连通分量的组合公式：与代数相关的平面图。我们对海藻代数的索引分析只需要基本的线性和抽象代数。事实上，本文的主要目标是向更广泛的读者介绍海藻代数，同时尽量减少对李理论中的专门语言和符号的吸引力。也就是说，我们提出了一些其他地方没有出现的结果，并且确实在引言中使用了更高级的语言来提供附加的上下文。