论文标题
海藻代数
Seaweed algebras
论文作者
论文摘要
谎言代数的索引是重要的代数不变，但众所周知，很难计算。然而，对于有指定义的海藻代数，可以根据“曲折”的连接组件的组合：与代数相关的平面图。我们对海藻代数的指数分析仅需要基本的线性和抽象代数。的确，这篇调查类型文章的主要目标是向更广泛的受众介绍海藻代数，对专业语言和谎言理论的符号的吸引力很小。也就是说，我们提出了几个没有出现在其他地方的结果，并且在简介提供附加背景下对更高级的语言确实具有吸引力。
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 survey-type 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.
