The Critical Groups of Adinkras Up to 2-Rank of Cayley Graphs

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 grap...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2024-02, Vol.31 (1)
Main Author: Yuen, Chi Ho
Format: Article
Language:English
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/11758