报告题目：The quantum symmetry in Hopf spin models determined by a Hopf ∗-subalgebra
报 告 人：蒋立宁 教授 北京理工大学
报告时间：2020年12月11日 14:00-15:00
报告地点：腾讯会议 ID：752 610 669 密码：1211
或直接点击链接入会：https://meeting.tencent.com/s/ce89eU2bRZwS
校内联系人：朱森 zhusen@jlu.edu.cn
报告摘要：
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 a unique *-homomorphism of
fulfilling the action of
on
such that
) and
commutant with each other.
报告人简介：
蒋立宁，北京理工大学数学与统计学院教授，博士生导师。1993年于江苏师范大学获学士学位，1996年于曲阜师范大学获硕士学位，1999年于北京大学数学学院获博士学位。2001年清华大学高等研究中心博士后出站后，进入北京理工大学工作，2007年晋升为教授。研究领域是泛函分析，主要研究兴趣集中在Hopf C^*代数及其表示理论、量子场代数及其内部对称结构以及非交换空间理论，并于2006年入选教育部新世纪优秀人才资助计划。
