Multiplicative preprojective algebras are 2-Calabi–Yau
Multiplicative preprojective algebras are 2-Calabi–Yau
We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw, are 2-Calabi-Yau algebras, in the case of quivers containing unoriented cycles.If the quiver is not itself a cycle, we show that the center is trivial, and hence the Calabi-Yau structure is unique.If the quiver is a cycle, we show …