We describe Calabi-Yau objects in the regular block of the (parabolic) BGG category $\mathcal{O}$ associated to a semi-simple finite dimensional complex Lie algebra. Each such object comes with a natural transformation from the Serre functor to a shifted identity whose evaluation at that object is an isomorphism.
Some homological properties of category O. IV
Some homological properties of category $\mathcal O$ for Lie superalgebras
Duality and Serre functor in homotopy categories
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