6 citations · 6 across the 7 of their papers we have counts for
7 papers
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…
Construction of Hopf algebroids
Yudai Otsuto, Youichi Shibukawa
For arbitrary algebras , we construct Hopf algebroids with base rings by means of satisfying suitable properties.
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…
Vertex--IRF correspondence and factorized L-operators for an elliptic R-operator
Youichi Shibukawa
As for an elliptic -operator which satisfies the Yang--Baxter equation, the incoming and outgoing intertwining vectors are constructed, and the vertex--IRF correspondence for th…