I-Quantum Groups and Hall algebras
[TMCSC]
Jan 04/07/09/12/15, 2021 9:00-11:00a.m.
ZOOM, Meeting ID: 990 5799 2629 Password: 525423
SPEAKERS
Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
ABSTRACT
The i-quantum groups arising from quantum symmetric pairs can be viewed as a natural generalization of Drinfeld-Jimbo quantum groups. Various fundamental constructions on quantum groups, including the q-Schur duality, R-matrix and canonical basis, have been generalized to i-quantum groups.
This mini-course addresses the Hall algebra realization of i-quantum groups recently developed by Ming Lu and Weiqiang Wang. This construction includes a reformulation of Bridgeland's Hall algebra realization for a whole quantum group. To that end, we introduce a class of finite-dimensional algebras called i-quiver algebras, and develop its representation theory. We shall also explain the i-divided powers, Serre presentation and braid group symmetries for i-quantum groups. Throughout, we shall focus on and work out various rank 1 and 2 examples.
SUPPORTED BY
Tianyuan Mathematical Center in Southwest China
School of Mathematics, Sichuan University
LECTURE NOTES
VIDEOS
- I-Quantum Groups and Hall algebras I
- 09:00 - 11:00, 2021-01-04 at ZOOM（线上）
- Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
- I-Quantum Groups and Hall algebras II
- 09:00 - 11:00, 2021-01-07 at ZOOM（线上）
- Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
- I-Quantum Groups and Hall algebras III
- 09:00 - 11:00, 2021-01-09 at ZOOM（线上）
- Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
- I-Quantum Groups and Hall algebras IV
- 09:00 - 11:00, 2021-01-12 at ZOOM（线上）
- Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)
- I-Quantum Groups and Hall algebras V
- 09:00 - 11:00, 2021-01-15 at ZOOM（线上）
- Weiqiang Wang (University of Virginia) & Ming Lu (Sichuan University)