论文标题
Lie代数和NS-Lie代数
Twisted Rota-Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras
论文作者
论文摘要
在本文中，我们在Lie代数上引入了扭曲的Rota-baxter操作员，作为扭曲的R-Matrices的操作员类似物。我们构建了一个合适的$ l_ \ infty $ -Algebra，其Maurer-Cartan元素由扭曲的Rota-baxter操作员给出。这使我们能够定义扭曲的Rota-baxter操作员的共同体学。该同胞可以将其视为特定代数的Chevalley-Eilenberg共同体，其系数合适。我们从共同体的角度研究了扭曲的旋转式运算符的变形。一些应用程序用于Reynolds操作员和扭曲的R-Matrices。接下来，我们引入了一种新的代数结构，称为NS-LIE代数，该结构与扭曲的Rota-Baxter操作员有关，就像前代代数与Rota-Baxter Operators有关的方式相同。我们通过考虑谎言代数上的模块上的扭曲的广义复合结构来结束本文。
In this paper, we introduce twisted Rota-Baxter operators on Lie algebras as an operator analogue of twisted r-matrices. We construct a suitable $L_\infty$-algebra whose Maurer-Cartan elements are given by twisted Rota-Baxter operators. This allows us to define cohomology of a twisted Rota-Baxter operator. This cohomology can be seen as the Chevalley-Eilenberg cohomology of a certain Lie algebra with coefficients in a suitable representation. We study deformations of twisted Rota-Baxter operators from cohomological points of view. Some applications are given to Reynolds operators and twisted r-matrices. Next, we introduce a new algebraic structure, called NS-Lie algebras, that are related to twisted Rota-Baxter operators in the same way pre-Lie algebras are related to Rota-Baxter operators. We end this paper by considering twisted generalized complex structures on modules over Lie algebras.
