6 citations · 6 across the 6 of their papers we have counts for
6 papers
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…
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…
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…
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…
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…
Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices
Anastasia Doikou, Bernard Rybolowicz, Paola Stefanelli
We present connections between left non-degenerate solutions of the set-theoretic braid equation and left shelves using Drinfel'd homomorphisms. We generalize the notion of affine…