论文标题
kupershmidt-nijenhuis在Malcev代数上的结构
Kupershmidt-Nijenhuis structures on pre-Malcev algebras
论文作者
论文摘要
我们在特征性零领域上研究了Kupershmidt操作员，Nijenhuis操作员和Kupershmidt-Nijenhuis结构。我们构建了几个复杂的Malcev前代数的新家族，这些家族不是二，三和四的维度前代数。我们使用线性操作员的兼容性来建立Kupershmidt操作员，Nijenhuis运算符和Kupershmidt-Nijenhuis结构之间的连接。此外，我们使用一种从计算理想理论的方法来表征Kupershmidt操作员和Nijenhuis运算符的几何结构上的三维复合物前代数。
We study Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on finite-dimensional pre-Malcev algebras over a field of characteristic zero. We construct several new families of complex pre-Malcev algebras that are not pre-Lie algebras in dimensions two, three and four. We use the compatibility of linear operators to establish connections between Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on pre-Malcev algebras. Moreover, we use a method from computational ideal theory to characterize the geometric structures of the varieties of Kupershmidt operators and Nijenhuis operators on a three-dimensional complex pre-Malcev algebra.
