Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras
Abstract
In this paper the conditions that when a Lie algebra is Nijenhuis are investigated. Furthermore all the Nijenhuis operators on sl2 under the standard Cartan-Weyl basis are given. On the other hand, the relations between the classical Yang-Baxter equation and Nijenhuis operators N on a Lie algebra and P on a Lie coalgebra are derived by means of the bialgebraic theory for Nijenhuis Lie algebras.
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