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Preprojective algebras and Calabi-Yau algebras
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OASW02 - Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras
Preprojective algebras are one of the central objects in representation theory. The preprojective algebra of a quiver Q is a graded algebra whose degree zero part is the path algebra kQ of Q, and each degree i part gives a distinguished class of representations of Q, called the preprojective modules. It categorifies the Coxeter groups as reflection functors, and their structure depends on the trichotomy of quivers: Dynkin, extended Dynkin, and wild. From homological algebra point of view, the algebra kQ is hereditary (i.e. global dimension at most one), and its preprojective algebra is 2-Calabi-Yau.
This talk is part of the Isaac Newton Institute Seminar Series series.
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