﻿ 2022年暑期代数短期课程计划-东北师范大学数学与统计学院

2022年暑期代数短期课程计划

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.

 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