4 papers · 1 filter
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…
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…