2017/09/23 by A. R. Armakan, Armakan, A. R., S. Silvestrov +3
Mathematics · #17B40 #17B56 #17B75 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B40 #msc:17B56 #msc:17B75
paper · pdf · doi:10.48550/arxiv.1709.08620
20 pages. arXiv admin note: substantial text overlap with arXiv:1709.06164
arxiv created 2017/09/23 · arxiv updated 2017/09/27
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 \mathfrakg by another hom-Lie algebra \mathfrakh and we discuss the case where \mathfrakh 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.