Hom-Lie-Rinehart algebras
Hom-Lie-Rinehart algebras
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DOI：
10.1080/00927872.2018.1424865
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发表时间：
2016-10
影响因子：
0.7
通讯作者：
A. Mandal;S. K. Mishra
中科院分区：
文献类型：
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作者：
A. Mandal;S. K. Mishra
摘要引入了Hom-Lie-Rinehart代数作为Hom-Lie代数体的代数模拟，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。在续篇中，我们分别利用某些阿贝尔扩张的自同构群和这些阿贝尔扩张在Hom-Lie-Rinehart代数范畴中的等价类来刻画低维上同调空间。我们还构造了与给定的Poisson代数和自同构相联系的Hom-Lie-Rinehart代数的典型例子。
ABSTRACT 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 characterization 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.