On the Iwasawa theory of Cayley graphs

التفاصيل البيبلوغرافية
العنوان: On the Iwasawa theory of Cayley graphs
المؤلفون: Ghosh, Sohan, Ray, Anwesh
سنة النشر: 2024
المجموعة: Mathematics
مصطلحات موضوعية: Mathematics - Number Theory, Mathematics - Combinatorics, Mathematics - Group Theory, 11R23, 05C25, 05C31, 05C50
الوصف: 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 $\mu$- and $\lambda$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish.
Comment: Version 1: 20 pages
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2405.04361
رقم الأكسشن: edsarx.2405.04361
قاعدة البيانات: arXiv