8 citations · 24 across the 18 of their papers we have counts for
20 papers
Surface Braid Invariants from Yang-Baxter Operators and Their Cohomology
Masahico Saito, Emanuele Zappala
Surface braids are a generalization of braids to surfaces in the 4-disk. They are described by planar graphs called charts, and sequences of braid words called braid systems, that…
Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
Masahico Saito, Emanuele Zappala
Yang-Baxter operators (YBOs) have been employed to construct quantum knot invariants. More recently, cohomology theories for YBOs have been independently developed, drawing inspira…
Deformation Cohomology for Braided Commutativity
Masahico Saito, Emanuele Zappala
Braided algebras are algebraic structures consisting of an algebra endowed with a Yang-Baxter operator, satisfying some compatibility conditions.Yang-Baxter Hochschild cohomology w…
Perturbative Expansion of Yang-Baxter Operators
Emanuele Zappala
We study the deformations of a wide class of Yang-Baxter (YB) operators arising from Lie algebras. We relate the higher order deformations of YB operators to Lie algebra deformatio…
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…
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…