The Calabi-Yau Property for Multiplicative Preprojective Algebras

Daniel Kaplan (Imperial College London)

Wednesday 13th February, 2019 16:00-17:00 Maths 311B


Multiplicative preprojective algebras were defined by Crawley-Boevey and Shaw in order to study the Deligne-Simpson problem. As with (additive) preprojective algebras, they arise through a symplectic-geometric study of the space of representations of a quiver. These algebras appeared recently in work of Etgu-Lekili in studying wrapped Fukaya categories of 4-manifolds built out of cotangent bundles using graphs. I suspect these algebras are 2-Calabi-Yau for non-Dynkin quivers and will sketch a proof in the case of quivers containing a cycle. Moreover, I'll outline an inductive argument, following work of Etingof-Eu, to reduce showing the 2-Calabi-Yau property for multiplicative preprojective algebras of extended Dynkin quivers. 

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