6 citations · 6 across the 7 of their papers we have counts for
5 papers · 1 filter
Structure groupoids of quiver-theoretic Yang-Baxter maps
Davide Ferri, Youichi Shibukawa
Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive…
Dynamical Reflection Maps
Ryosuke Ashikaga, Youichi Shibukawa
In this paper, by making use of category theory, we construct dynamical reflection maps, solutions to a version of the reflection equation associated with suitable dynamical Yang-B…
Dynamical Yang-Baxter maps and Hopf algebroids associated with s-sets
Noriaki Kamiya, Youichi Shibukawa
An s-set is an algebraic generalization of the regular s-manifold introduced by Kowalski, one of the generalized symmetric spaces in differential geometry. We prove that suitable s…
FRT Construction for Dynamical Yang-Baxter Maps
Youichi Shibukawa, Mitsuhiro Takeuchi
Notions of an (H, X)-bialgebroid and of its dynamical representation are proposed. The dynamical representations of each (H, X)-bialgebroid form a tensor category. Every dynamical…
Dynamical Yang-Baxter Maps with an Invariance Condition
Youichi Shibukawa
By means of left quasigroups L=(L, .) and ternary systems, we construct dynamical Yang-Baxter maps associated with L, L, and (.) satisfying an invariance condition that the binary…