论文标题
左对称Rinehart代数的同时和变形
Cohomology and Deformations of left-symmetric Rinehart Algebras
论文作者
论文摘要
我们引入了左对称Rinehart代数的概念，该代数是左对称代数的概括。左乘法产生相应的亚粘合物lie-rinehart代数的表示。我们在lie-rinehart代数上构建了来自O-Operator的左对称Rinehart代数。我们广泛研究了左对称Rinehart代数的表示。此外，我们研究了左对称rinehart代数的变形，该代数由变形辅助学中的第二个共同学类别控制。我们还提供了O-operators和Nijenhuis操作员在左2级代数方面的关系。
We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct left-symmetric Rinehart algebra from O-operators on Lie-Rinehart algebra. We extensively investigate representations of a left-symmetric Rinehart algebras. Moreover, we study deformations of left-symmetric Rinehart algebras, which is controlled by the second cohomology class in the deformation cohomology. We also give the relationships between O-operators and Nijenhuis operators on left-symmetric Rinehart algebras.
