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Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r-matrices. A super dynamical r-matrix r satisfies the zero weight condition if [h⊗ 1 + 1⊗ h, r(λ)] = 0 for all h ∈ h, λ ∈ h∗. In this paper we explicitly quantize zero-weight super dynamical r-matrices with zero coupling constant for the Lie superalgebra gl(m,n). We also answer some questions about super dynamical R-matrices. In particular, we prove a classification theorem and offer some support for one particular interpretation of the super Hecke condition.

On the quantization of zero-weight super dynamical 𝑟-matrices