Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) 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)
[ 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.