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• W3100437640 abstract "In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation. Then we introduce the notion of a Kupershmidt-(dual-)Nijenhuis structure on a Lie algebra with a representation, which is a generalization of the $r$-$n$ structure ($r$-matrix-Nijenhuis structure) introduced by Ravanpak, Rezaei-Aghdam and Haghighatdoost. We show that a Kupershmidt-(dual-)Nijenhuis structure gives rise to a hierarchy of Kupershmidt operators. Finally, we define a Rota-Baxter-Nijenhuis structure to be a Kupershmidt-Nijenhuis structure on a Lie algebra with respect to the adjoint representation, and study the relation between Rota-Baxter-Nijenhuis structures and $r$-matrix-Nijenhuis structures." @default.
• W3100437640 created "2020-11-23" @default.
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• W3100437640 date "2018-08-01" @default.
• W3100437640 modified "2023-10-06" @default.
• W3100437640 title "Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation" @default.
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• W3100437640 doi "https://doi.org/10.1063/1.5027371" @default.
• W3100437640 hasPublicationYear "2018" @default.
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