论文标题
$ k $ - nilpotent lie lie代数的分类与图形相关
Classification of $K$-forms in nilpotent Lie algebras associated to graphs
论文作者
论文摘要
鉴于一个简单的无方向图，可以从中构建一个$ c $ - 步骤的nilpotent lie代数，每$ c \ geq 2 $和任何字段$ k $，尤其是在真实和复数上。这些谎言代数构成了几何和代数中重要的示例类别，并且将其属性链接到定义图很有趣。在本文中，我们在这些真实且复杂的代数中为任何子场$ k \ subset \ mathbb {c} $从图表的结构中分类了$ k $ forms的同构类别。作为一种应用，我们表明，与同构的理性数量始终是一个或无限的，而前者是正确的，并且仅当thraph型自动形态是由thrans置产生的。
Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of examples in geometry and algebra, and it is interesting to link their properties to the defining graph. In this paper, we classify the isomorphism classes of $K$-forms in these real and complex Lie algebras for any subfield $K \subset \mathbb{C}$ from the structure of the graph. As an application, we show that the number of rational forms up to isomorphism is always one or infinite, with the former being true if and only if the group of graph automorphisms is generated by transpositions.
