论文标题
特征值和丁基丁基的关键群体
Eigenvalues and Critical Groups of Adinkras
论文作者
论文摘要
Adinkras是用于研究物理学超对称性的签名图。我们提供了这些物体的介绍，并研究其签名的邻接性和签名的拉普拉斯矩阵的特性。这些矩阵每个矩阵都完全具有两个不同的特征值（相等的多重性），这使得丁基拉斯与强规图的概念密切相关。我们还研究了丁基的关键群体，尤其是确定它们的奇数成分。使用了一种新型的独立感兴趣技术，该技术考虑了多项式环上的关键群体。
Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making Adinkras closely related to the notions of strongly regular graphs. We also study the critical groups of Adinkras, and in particular determine their odd components. A novel technique of independent interest is used which considers critical groups over polynomial rings.
