Abstract
In this paper, we introduce the cohomology of Rota-Baxter operators on Lie superalgebras. We define the cohomology of a Rota-Baxter operator R as the Chevalley Eilenberg cohomology of a certain Lie superalgebra induced by R with coefficients in a suitable representation. Then, we give the classification of the homogeneous Rota-Baxter operators of weight 0 on the Witt superalgebras. To apply our approach, we construct pre-Lie superalgebras from the homogeneous Rota-Baxter operators of weight 0 and their subadjacent Lie superalgebras.
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