The classical Yang-Baxter equation as formulated by Semenov-Tyan-Shanskii is generalized to the case of Lie superalgebras [Formula: see text], for Grassmann even Yang-Baxter operators ℛ. When ℛ is “unitary” with respect to a super trace form defined on [Formula: see text], we prove the existence of two natural Poisson brackets on the dual [Formula: see text]*. If [Formula: see text] is the infinite-dimensional Lie superalgebra of N=1 super pseudodifferential operators, we recover the super Gel’fand-Dikii brackets underlying the N=1 super KP hierarchy and its reductions.
