Rota–Baxter operators on the simple Jordan superalgebra $D_t$

Up to conjugation by an automorphism, we describe the Rota–Baxter operators of weight zero or nonzero on the simple four-dimensional Jordan superalgebra $D_t$ over an algebraically closed field of characteristic $0$. The description includes the classification of all decompositions of $D_t$ into a direct sum of two subalgebras.