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Tokyo-Nagoya Algebra Seminar
Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～
| Organizer(s) | Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi |
|---|
2025/04/15
10:30-12:00 Room # ハイブリッド開催/128 (Graduate School of Math. Sci. Bldg.)
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
[ Abstract ]
Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
[ Reference URL ]Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
