My research areas are: representation theory of quantum groups; elliptic R-operators; and dynamical Yang-Baxter maps. The dynamical Yang-Baxter map is a solution to the quantum Yang-Baxter equation on a suitable tensor category. This concept induces bialgebroids and tensor categories of their dynamical representations. My interest is to clarify relations between them and to construct Hopf algebroids by means of the dynamical Yang-Baxter maps.
- Y. Shibukawa: Dynamical Yang-Baxter maps, Int. Math. Res. Not. 2005(36) (2005) 2199-2221.
- Y. Shibukawa, M. Takeuchi: FRT construction for dynamical Yang-Baxter maps, J. Alg. 323 (2010) 1698-1728.
- N. Kamiya, Y. Shibukawa: Dynamical Yang-Baxter maps associated with homogeneous pre-systems, J. Gen. Lie Theory Appl. 5 (2011) Art.ID G110106, 9pp.
- D. K. Matsumoto, Y. Shibukawa: Quantum Yang-Baxter equation, braided semigroups, and dynamical Yang-Baxter maps, Tokyo J. Math. 38 (2015) 227-237.
- Y. Shibukawa: Hopf algebroids and rigid tensor categories associated with dynamical Yang-Baxter maps, J. Alg. 449 (2016) 408-445.