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トポロジー火曜セミナー
過去の記録 ～12/07｜次回の予定｜今後の予定 12/08～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2017年01月17日(火)
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
杉山 聡 氏 (東京大学大学院数理科学研究科)
On an application of the Fukaya categories to the Koszul duality (JAPANESE)
Tea: Common Room 17:00-17:30
杉山 聡 氏 (東京大学大学院数理科学研究科)
On an application of the Fukaya categories to the Koszul duality (JAPANESE)
[ 講演概要 ]
In this talk, we compute an A∞-Koszul dual of path algebras with relations over the directed An-type quivers via the Fukaya categories of exact Riemann surfaces.
The Koszul duality is originally a duality between certain quadratic algebras called Koszul algebras. In this talk, we are interested in the case when A is not a quadratic algebra, i.e. the case when A is defined as a quotient algebra of tensor algebra devided by higher degree relations.
The definition of Koszul duals for such algebras, A∞-Koszul duals, are given by some people, for example, D. M. Lu, J. H. Palmieri, Q. S. Wu, J. J. Zhang. However, the computation for a concrete examples is hard. In this talk, we use the Fukaya categories of exact Riemann surfaces to compute A∞-Koszul duals. Then, we understand the Koszul duality as a duality between higher products and relations.
In this talk, we compute an A∞-Koszul dual of path algebras with relations over the directed An-type quivers via the Fukaya categories of exact Riemann surfaces.
The Koszul duality is originally a duality between certain quadratic algebras called Koszul algebras. In this talk, we are interested in the case when A is not a quadratic algebra, i.e. the case when A is defined as a quotient algebra of tensor algebra devided by higher degree relations.
The definition of Koszul duals for such algebras, A∞-Koszul duals, are given by some people, for example, D. M. Lu, J. H. Palmieri, Q. S. Wu, J. J. Zhang. However, the computation for a concrete examples is hard. In this talk, we use the Fukaya categories of exact Riemann surfaces to compute A∞-Koszul duals. Then, we understand the Koszul duality as a duality between higher products and relations.
