2019 Thematic Program (IV)
Graded algebras related to noncommutative projective space
October , 2020
W303 School of Mathematics, Sichuan University
This mini-course will cover the following topics:
1. Artin-Schelter regular algebras and Calabi-Yau algebras
(1) Introduce $A_\infty$-algebras, and then prove the theorem of the Frobenius property of the Ext-algebras of Artin-Schelter regular algebras.
(2) Homological integrals of Artin-Schelter Gorenstein algebras and the Nakayama automorphisms.
(3) Calabi-Yau algebras.
2. Koszul duality and BGG correspondence
(1) Koszul dualities induce BGG correspondence (DG version).
(2) PBW deformations of Koszul algebras and Nonhomogeneous Koszul dualities.
3. Noncommutative Auslander Theorem and McKay correspondence
(1) Hopf actions on Artin-Schelter regular algebras.
(2) Noncommutative Auslander Theorem and Noncommutative resolutions.
(3) Noncommutative McKay correspondence.
4. Noncommutative matrix factorizations and hypersurfaces
(1) Noncommutative matrix factorizations and their relations with singularities of hypersurfaces.
(2) Deformations of Koszul Frobenius algebras and noncommutative quadrics.