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Tuesday Seminar on Topology
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2017/01/17
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Satoshi Sugiyama (The University of Tokyo)
On an application of the Fukaya categories to the Koszul duality (JAPANESE)
Satoshi Sugiyama (The University of Tokyo)
On an application of the Fukaya categories to the Koszul duality (JAPANESE)
[ Abstract ]
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.
