Report title: The quantum symmetry in Hopf spin models determined by a Hopf ∗-subalgebra

Reporter: Professor Jiang Lining, Beijing Institute of Technology

Reporting time: 14:00-15:00, December 11, 2020

Report location: Tencent meeting ID: 752 610 669 Password: 1211

Or click the link directly to join the conference: https://meeting.tencent.com/s/ce89eU2bRZwS

School contact: Zhu Sen zhusen@jlu.edu.cn

Report summary:

Let be a finite dimensional Hopf-algebra, be a Hopf *-subalgebra of. One considers the structure of the observable algebra and the symmetry of field algebra in Hopf spin models determined by. The commutation relations between links and sites give rise to the observable algebra. Further, using the iterated tensor product of finite *-algebras, one can prove that the observable algebra is * -isomorphic to, where denotes the dual of, and includes a -inductive limit procedure. The field algebra follows from the coaction of the quantum double on the observable algebra, defined as the crossed product. Here is the bicrossed product of the opposite dual of and with respect to the coadjoint representation latter acting on the former and vice versa. This product yields a-invariant subalgebra of which is exactly the observable algbra. Moreover, a duality between and implemented by a *-representation of is obtained. In other words, there exists au nique *-homomorphism of fulfilling the action of on such that) and commutant with each other.

Brief introduction of the speaker:

Jiang Lining is a professor and doctoral supervisor at the School of Mathematics and Statistics, Beijing Institute of Technology. He received a bachelor's degree from Jiangsu Normal University in 1993, a master's degree from Qufu Normal University in 1996, and a doctorate degree from the School of Mathematics, Peking University in 1999. After being a postdoctoral fellow at the Advanced Research Center of Tsinghua University in 2001, he entered Beijing Institute of Technology and was promoted to professor in 2007. The research field is functional analysis, and his main research interests are in Hopf C^* algebra and its representation theory, quantum field algebra and its internal symmetric structure, and non-commutative space theory. In 2006, he was selected into the New Century Excellent Talent Funding Program of the Ministry of Education.