The Critical Groups of Adinkras up to 2-Rank of Cayley Graphs
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Adinkras are graphical gadgets introduced by physicists to study supersymmetry, which can be thought of as the Cayley graphs for supersymmetry algebras. Improving the result of Iga et al., we determine the critical group of an Adinkra given the 2-rank of the Laplacian of the underlying Cayley graph. As a corollary, we show that the critical group is independent of the signature of the Adinkra. The proof uses the monodromy pairing on these critical groups.
| Originalsprog | Engelsk |
|---|---|
| Artikelnummer | P1.38 |
| Tidsskrift | Electronic Journal of Combinatorics |
| Vol/bind | 31 |
| Udgave nummer | 1 |
| Antal sider | 9 |
| ISSN | 1077-8926 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
The author was supported by the Trond Mohn Foundation project “Algebraic and Topological Cycles in Complex and Tropical Geometries” at the University of Oslo; he also acknowledges the support of the Centre for Advanced Study (CAS) in Oslo, Norway, which funded and hosted the Young CAS research project “Real Structures in Discrete, Algebraic, Symplectic, and Tropical Geometries” during the 2021/2022 and 2022/2023 academic years. The author thanks Kevin Iga for reading an early draft and explaining the remarks in [11], and the anonymous referee for the helpful suggestions.
Publisher Copyright:
© The author. Released under the CC BY-ND license (International 4.0).
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