Hom-Lie-Rinehart代数
Hom-Lie-Rinehart Algebras
摘要：
引入hom-Lie-Rinehart代数作为hom-Lie代数胚的代数类似物，并通过考虑系数模系统地刻画了上同调复形。我们定义了hom-Lie-Rinehart代数的扩张的概念。其次，我们分别利用一类交换扩张的自同构自同构群和这些交换扩张在hom-Lie-Rinehart代数范畴中的等价类，给出了低维上同调空间的一个刻画.我们还构造了一个典型的例子hom-Lie-Rinehart代数相关联的一个给定的泊松代数和一个自同构。
英文摘要：
We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In the sequel, we deduce a characterisation of low dimensional cohomology spaces in terms of the group of automorphisms of certain abelian extension and the equivalence classes of those abelian extensions in the category of hom-Lie-Rinehart algebras, respectively. We also construct a canonical example of hom-Lie-Rinehart algebra associated to a given Poisson algebra and an automorphism.
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