论文标题
2步nilpotent Lie代数中的Abelian因子由图形构建
Abelian Factor in 2-step Nilpotent Lie Algebras Constructed from Graphs
论文作者
论文摘要
我们考虑了与雷在2016年构建的可能重复的边缘标签相关的图形相关的真实的2步公制的谎言代数。我们确定图表内的EGDE标记的结构如何促进这些代数中的Abelian因子。此外，我们明确计算了与某些图形族相关的2步nilpotent Lie代数的Abelian因子，例如恒星图，循环，Schreier图和正确的边缘色图。在某些情况下，我们还研究了这些代数的奇异性特性。
We consider real 2-step metric nilpotent Lie algebras associated to graphs with possibly repeated edge labels as constructed by Ray in 2016. We determine how the structure of the egde labeling within the graph contributes to the abelian factor in these Lie algebras. Furthermore, we explicitly compute the abelian factor of the 2-step nilpotent Lie algebras associated with some families of graphs such as star graphs, cycles, Schreier graphs, and properly edge-colored graphs. We also study the singularity properties of these Lie algebras in certain cases.
