SHIBUKAWA, Youichi
 Research Field
 Algebra
 Position
 Associate Professor
 Organization
 Department of Mathematics
 Research Interest
 Infinite analysis; Integrable systems
 Research Activities

My research areas are: representation theory of quantum groups; elliptic Roperators; and dynamical YangBaxter maps. The dynamical YangBaxter map is a solution to the quantum YangBaxter 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 YangBaxter maps.
 Papers:
 [1] Y. Shibukawa: Dynamical YangBaxter maps, Int. Math. Res. Not. 2005(36) (2005) 21992221.
 [2] Y. Shibukawa, M. Takeuchi: FRT construction for dynamical YangBaxter maps, J. Alg. 323 (2010) 16981728.
 [3] N. Kamiya, Y. Shibukawa: Dynamical YangBaxter maps associated with homogeneous presystems, J. Gen. Lie Theory Appl. 5 (2011) Art.ID G110106, 9pp.
 [4] D. K. Matsumoto, Y. Shibukawa: Quantum YangBaxter equation, braided semigroups, and dynamical YangBaxter maps, Tokyo J. Math. 38 (2015) 227237.
 [5] Y. Shibukawa: Hopf algebroids and rigid tensor categories associated with dynamical YangBaxter maps, J. Alg. 449 (2016) 408445.
 Keywords
 (Dynamical) YangBaxter equation, (Elliptic) Roperator, Representation theory of quantum groups