课程名称：Simple representations of the Virasoro Algebra

授课人：赵开明教授（加拿大劳瑞尔大学）

授课方式：腾讯会议

课程简介：

This is a 15-hour mini-course for graduate students and young Lie algebra researchers. I will first use one or two lectures reviewing results on representations of the Virasoro algebra established before 2000. Then we will present various simple weight and non-weight representations of the Virasoro algebra, including classification of simple restricted modules over the Virasoro algebra. Its goal is to prepare the students for further study on the Virasoro algebra and its applications.

Course description: The course will recall the structure theory and representation theory of the Virasoro algebra. Then we introduce various simple weight and non-weight representations of the Virasoro algebra achieved after 2000. We will also post some open problems on various simple weight and non-weight representations of the Virasoro algebra. The contents of this course come from the textbook

[V. Kac, A. Raina, N. Rozhkovskaya, Bombay lectures on highest weight representations of infinite dimensional Lie algebras. Second edition. Advanced Series in Mathematical Physics, 29. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. xii+237 pp.]

and from scattered recent research papers, including

• Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming Fraction representations and highest-weight-like representations of the Virasoro algebra. J. Algebra 387 (2013), 68–86.

• Chen, Hongjia; Guo, Xiangqian; Zhao, Kaiming Tensor product weight modules over the Virasoro algebra. J. Lond. Math. Soc. (2) 88 (2013), no. 3, 829–844.

• Mazorchuk, Volodymyr; Zhao, Kaiming Simple Virasoro modules which are locally finite over a positive part. Selecta Math. (N.S.) 20 (2014), no. 3, 839–854.

• Lü, Rencai; Zhao, Kaiming A family of simple weight modules over the Virasoro algebra. J. Algebra 479 (2017), 437–460.

课程安排：

日期	时间	腾讯会议 ID
2022/8/14周日	8:00-10:30	会议号：317-9313-7599，密码：2022
2022/8/21周日	8:00-10:30
2022/8/28周日	8:00-10:30
2022/9/4周日	8:00-10:30
2022/9/11周日	8:00-10:30

授课人简介：

赵开明，加拿大劳瑞尔大学教授、博导，河北师范大学兼职教授、博导，中国科学院“百人计划”入选者。主要从事李代数、非交换代数等领域的研究工作，在Adv. Math.、Proc. London Math. Soc.、Trans. Amer. Math. Soc.、Math. Z.、Israel J. Math.、Selecta Math.(N.S.)、J. Algebra、J. Pure Appl. Algebra等杂志发表高水平学术论文一百多篇，其研究成果受到国际同行的高度评价。主持完成多项加拿大研究理事会基金项目和多项国家面上项目，是国际代数学领域有重要影响的专家。