2012/09/26 by Casas, J. M., Insua, M. A., Pacheco, N.
#17A30 #17B55 #17B60 #18G35 #18G60 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1209.5887
We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting, because of the composition of two central extensions is not central. This fact leads to introduce the notion of universal α-central extension. Classical results as the existence of a universal central extension of a perfect Hom-Lie algebra remains true, but others as the central extensions of the middle term of a universal central extension is split only holds for α-central extensions. A homological characterization of universal (α)-central extensions is given.