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Frobenius algebras and fractional Calabi-Yau categories

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If you have a question about this talk, please contact Gareth Tracey.

Given a quiver we consider two algebras: its path algebra and its preprojective algebra. If the quiver is Dynkin, i.e., its underlying graph is a simply laced Dynkin diagram, then both algebras have nice properties: the derived category of the path algebra is fractionally Calabi-Yau, and the preprojective algebra is Frobenius with a Nakayama automorphism of finite order. One can show that, if stated carefully, these properties are equivalent. I will give an introduction to the concepts above and, time permitting, will describe some of the ingredients of the proof of this equivalence.

This talk is part of the Birmingham Algebra Seminar series.

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