Eigenvalues and Critical Groups of Adinkras
Combinatorics
2022-02-08 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2202.02821,
title = {Eigenvalues and Critical Groups of Adinkras},
author = {Kevin Iga and Caroline Klivans and Jordan Kostiuk and Chi Ho Yuen},
journal= {arXiv preprint arXiv:2202.02821},
year = {2022}
}