论文标题
kupershmidt-（双 - ）nijenhuis结构，在谎言代数上具有代表性
Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation
论文作者
论文摘要
在本文中，首先，我们研究了具有代表性的Lie代数的无限变形，并介绍了Nijenhuis对的概念，该概念给出了带有表示的Lie代数的微不足道变形。然后，我们介绍了带有代表性的Lie代数上的Kupershmidt-（dual-）nijenhuis结构的概念，这是对由$ r $ $ n $结构（$ r $ -r $ -matrix-nijenhuis结构）的概括，该结构由Ravanpak，Rezae-agaghdam和Haghighatdoers和Haghighatdoers引入。我们表明，kupershmidt-（双）nijenhuis结构产生了Kupershmidt操作员的层次结构。最后，我们将rota-baxter-nijenhuis结构定义为kupershmidt-nijenhuis在lie代数相对于伴随表示方面的结构，并研究了rota-baxter-baxter-nijenhuis结构与$ r $ r $ -Matrix-Nijenhuis结构之间的关系。
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.
