3 papers
math.QA2025
Combinatorial twists in gl_n Yangians
Anastasia Doikou
We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via…
math.RA2024
Parametric reflection maps: an algebraic approach
Anastasia Doikou, Marzia Mazzotta, Paola Stefanelli
We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks…
math-ph2024
Self-distributive structures, braces & the Yang-Baxter equation
Anastasia Doikou
The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. T…