Admissible Dissections of Surfaces and Piano Algebras

Admissible dissections of marked surfaces were used to classify gentle algebras and to provide a geometric model for their derived categories by Opper-Plamondon-Schroll. We introduce the notion of an extended admissible dissection of a marked surface, and the piano algebra associated to an extended admissible dissection. We will discuss how the set of extended admissible diagrams of a marked disc without punctures is in bijection to the set of equivalence classes of a subset of classical generators of a Paquette-Yıldırım category. Further, we will see how the perfect derived category of a particular piano algebra is additively equivalent to a Paquette-Yıldırım category.

Link: https://unipd.zoom.us/j/82518660070?pwd=RUpxL1FnZG9yVzFrOCtrM0xYMEZaZz09

Meeting ID: 825 1866 0070

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