Report title: Generalized Frobenius category and semi-derived Ringel-Hall algebra
Reporter: Professor Peng Liangang, School of Mathematics, Sichuan University
Reporting time: 14:00-15:00, September 22, 2020
Report location: Tencent Conference ID: 828 498 860
Or click the link to join the meeting directly:
https://meeting.tencent.com/s/GzgyS1YT1kJp
School contact: Sun Xiaosong sunxs@jlu.edu.cn
Report summary:
In 2013, T. Bridgeland used the localization of the Ringel-Hall algebra of the 2-period complex of the projective modulus to realize the overall quantum envelope algebra. After that, M. Gorsky used two methods to generalize the construction of T. Bridgeland to define the so-called semi-derived Hall algebra. One is to use the Frobenius category, and its construction is not essentially different from that of T. Bridgeland, and the other requires stronger Conditions and its construction is not very straightforward. Note that their construction of 2-periodic complexes cannot include important genetic categories such as weighted projective line cohesive categories. In cooperation with Lu Ming, we defined a modified Ringel- for any genetic category 2-periodic complex category. Hall algebra. In this report, we define the generalized Frobenius category and semi-derived Ringel-Hall algebra to unify all the above constructions under one framework. This is a collaborative work with Lin Ji.
Brief introduction of the speaker:
Peng Liangang is a professor and doctoral supervisor at the School of Mathematics, Sichuan University. In 1991, he received his Ph.D degree from Beijing Normal University (supervisor Professor Liu Shaoxue). National Outstanding Youth Fund, Cross (New) Century Excellent Talents of the Ministry of Education, Excellent Young Teacher Funding Program of the Ministry of Education, Outstanding Experts with Outstanding Contributions at the Provincial and Ministerial Level, Winner of the German Humboldt Fund, Dean of the School of Mathematics of Sichuan University, National Higher Education Member of the steering committee of science mathematics and mechanics. The research direction is algebraic representation theory and Lie theory. Presided over the National Natural Science Foundation of China, the Doctoral Fund of the Ministry of Education, and the National Science Base of the Ministry of Education to create famous-brand courses. Participated in the "Frontier Issues in Core Mathematics" project of the Ministry of Science and Technology. He published dozens of academic papers in important journals such as Invent. Math., J. London Math. Soc., J. Algebra, and his research results won the second prize of Science and Technology Progress Award of the Ministry of Education.
