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math-ph2025
Braided finite automata and representation theory
Anastasia Doikou
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxet…
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…
math-ph2024
Parametric set-theoretic Yang-Baxter equation: p-racks, solutions & quantum algebras
Anastasia Doikou
The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of c…