Pivotal structures of the Drinfeld center of a finite tensor category

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We show that pivotal structures of the Drinfeld center of a finite tensor category C are in bijection with the set of equivalence classes of a pair (β,j) consisting of an invertible object β of C and a monoidal natural transformation jX:β⊗X⊗β⁎→X⁎⁎ (X∈C). As an application of techniques used to prove the main result, we also obtain a non-semisimple analogue of a categorification of the Rosenberg-Zelinsky exact sequence for fusion categories given by Galindo and Plavnik