Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation
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 - structure (-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 -matrix-Nijenhuis structures.
Keywords
Cite
@article{arxiv.2004.10065,
title = {Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation},
author = {Yuwang Hu and Jiefeng Liu and Yunhe Sheng},
journal= {arXiv preprint arXiv:2004.10065},
year = {2020}
}
Comments
16 pages