Abstract
Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r r -matrices. A super dynamical r r -matrix r r satisfies the zero weight condition if [ h â 1 + 1 â h , r ( λ ) ] = 0 for all h â h , λ â h â . \begin{equation*} [h\otimes 1 + 1 \otimes h, r(\lambda )] = 0 \text { for all } h \in \mathfrak {h}, \lambda \in \mathfrak {h}^*. \end{equation*} In this paper we explicitly quantize zero-weight super dynamical r r -matrices with zero coupling constant for the Lie superalgebra g l ( m , n ) \mathfrak {gl}(m,n) . We also answer some questions about super dynamical R R -matrices. In particular, we prove a classification theorem and offer some support for one particular interpretation of the super Hecke condition.
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