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math.QA2023
Yang-Baxter Solutions from Categorical Augmented Racks
Masahico Saito, Emanuele Zappala
An augmented rack is a set with a self-distributive binary operation induced by a group action, and has been extensively used in knot theory. Solutions to the Yang-Baxter equation…
math.RT2023
On the representation theory of cyclic and dihedral quandles
Mohamed Elhamdadi, Prasad Senesi, Emanuele Zappala
Quandle representations are homomorphisms from a quandle to the group of invertible matrices on some vector space taken with the conjugation operation. We study certain families of…
math.QA2023
Yang-Baxter Hochschild Cohomology
Masahico Saito, Emanuele Zappala
Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild co…