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東京名古屋代数セミナー
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 担当者 | 阿部 紀行、Aaron Chan、伊山 修、行田 康晃、淺井 聡太、高橋 亮 |
|---|---|
| セミナーURL | http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html |
2025年04月15日(火)
10:30-12:00 数理科学研究科棟(駒場) ハイブリッド開催/128号室
Parth Shimpi 氏 (University of Glasgow)
Torsion pairs for McKay quivers (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Parth Shimpi 氏 (University of Glasgow)
Torsion pairs for McKay quivers (English)
[ 講演概要 ]
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
[ 講演参考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
