On the Iwasawa theory of Cayley graphs Article Swipe
Related Concepts
Cayley graph
Iwasawa theory
Mathematics
Algebra over a field
Pure mathematics
Discrete mathematics
Graph
Abelian group
Sohan Ghosh
,
Anwesh Ray
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.04361
· OA: W4396815103
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2405.04361
· OA: W4396815103
This paper explores Iwasawa theory from a graph theoretic perspective, focusing on the algebraic and combinatorial properties of Cayley graphs. Using representation theory, we analyze Iwasawa-theoretic invariants within $\mathbb{Z}_\ell$-towers of Cayley graphs, revealing connections between graph theory, number theory, and group theory. Key results include the factorization of associated Iwasawa polynomials and the decomposition of $μ$- and $λ$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish.
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