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Extensions of hom-Lie color algebras
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2019-07-12 , DOI: 10.1515/gmj-2019-2033
Abdoreza Armakan 1 , Sergei Silvestrov 2 , Mohammad Reza Farhangdoost 1
Affiliation  

In this paper we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie algebra $\mathfrak{g}$ by another hom-Lie algebra $\mathfrak{h}$ and we discuss the case where $\mathfrak{h}$ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i. e. we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.

中文翻译:

hom-Lie 颜色代数的扩展

在本文中,我们研究给定 hom-Lie 颜色代数的(非阿贝尔)扩展,并提供扩展的几何解释。特别地,我们用另一个 hom-Lie 代数 $\mathfrak{h}$ 刻画了一个 hom-Lie 代数 $\mathfrak{g}$ 的扩展,并且我们讨论了 $\mathfrak{h}$ 没有中心的情况。我们还处理了微分几何中可能的扩展的协变外部导数、Chevalley 导数、曲率和 Bianchi 恒等式的设置。此外,我们发现了 hom-Lie 颜色代数的扩展存在的上同调障碍,即我们表明,为了有一个可扩展的 hom-Lie 颜色代数,应该存在第三个上同调的一个微不足道的成员。
更新日期:2019-07-12
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