4 papers
Lie Quandles, Leibniz Racks and Noether's First Theorem
Mohamed Elhamdadi, Bryce Virgin
In [Self-distributive structures in physics. Internat. J. Theoret. Phys. 64 (2025), no. 3, Paper No. 73], Fritz was motivated by the structure of Hamiltonian/Heisenberg mechanics t…
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…
Connections between conjugation quandles and their underlying groups via residual finiteness and the Hopf property
Mohamed Elhamdadi, Jan Kim
We prove that if a conjugation quandle is Hopfian, then its underlying group is also Hopfian. We also show that the converse does not hold by providing an example. This highlights…
Yang-Baxter Equation and Related Algebraic Structures
Valeriy Bardakov, Mohamed Elhamdadi, Mahender Singh
In the 1990s, Drinfel'd proposed the study of set-theoretical solutions to the quantum Yang-Baxter equation, initiating a line of research that has since garnered substantial atten…