7 papers
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…
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…
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…
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…
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…
Twisted Yang-Baxter sets, cohomology theory, and application to knots
Mohamed Elhamdadi, Manpreet Singh
We introduce twisted set-theoretic Yang-Baxter solutions and develop an associated cohomology theory, which extends the standard cohomology theory of Yang-Baxter solutions. By empl…
Bridging colorings of virtual links from virtual biquandles to biquandles
Mohamed Elhamdadi, Manpreet Singh
A biquandle is a solution to the set-theoretical Yang-Baxter equation, which yields invariants for virtual knots such as the coloring number and the state-sum invariant. A virtual…