A matrix theory introduction to seaweed algebras and their index

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-06-19 DOI:10.1016/j.exmath.2023.06.001

Alex Cameron , Vincent E. Coll Jr. , Nicholas Mayers , Nicholas Russoniello

引用次数: 0

Abstract

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.

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海藻代数及其索引的矩阵论导论

李代数的指标是一个重要的代数不变量，但它的计算是出了名的困难。然而，对于具有暗示性名称的海藻代数，指数的计算可以简化为基于“曲流”的连接组件的组合公式:与代数相关的平面图。我们对海藻代数的指数分析只需要基本的线性代数和抽象代数。实际上，本文的主要目标是向更广泛的读者介绍海藻代数，并尽量减少对李理论中的专门语言和符号的吸引力。这就是说，我们提出了几个没有出现在其他地方的结果，并且在引言中确实需要更高级的语言来提供额外的上下文。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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