A Nijenhuis pre-Lie bialgebra framework is introduced, connecting Nijenhuis operators on pre-Lie algebras to S-equations, O-operators, and ultimately to Nijenhuis Lie bialgebras.
Bai, Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation
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Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation
A Nijenhuis pre-Lie bialgebra framework is introduced, connecting Nijenhuis operators on pre-Lie algebras to S-equations, O-operators, and ultimately to Nijenhuis Lie bialgebras.