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Super solutions of the dynamical Yang-Baxter equation

Authors:	Gizem Karaali

Institution:	Department of Mathematics, University of California, Santa Barbara, California 93106

Abstract:	Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical matrices. A super dynamical matrix satisfies the zero weight condition if $\displaystyle h\otimes 1 + 1 \otimes h, r(\lambda)] = 0$ for all $\displaystyle h \in \mathfrak{h}, \lambda \in \mathfrak{h}^*.$ In this paper we classify super dynamical matrices with zero weight.

Keywords:	Dynamical $r-$matrices the dynamical Yang-Baxter equation Lie superalgebras

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