Showing 2026Show all
3 papers · 1 filter
math.GT2026
Fourier Analysis and Idempotents in Quandle Algebras
Mohamed Elhamdadi, Luc Ta, Bryce Virgin
In 2023, the first author, Nunez, Singh, and Swain [10] formulated an analogue of Kaplansky's idempotent conjecture for integral quandle rings. In this paper, we develop a new Four…
math.QA2026
Lie Quandles, Leibniz Racks and Noether's First Theorem
Mohamed Elhamdadi, Bryce Virgin
In [Internat. J. Theoret. Phys. 64 (2025), 73, 10 pages], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics to define the notion of ''Lie quandle'', which he…
math.RA2026
Idempotents and Powers of Ideals in Quandle Rings
Valeriy Bardakov, Mohamed Elhamdadi
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a sem…