Current Hom-Lie algebras
Keywords:Current Hom-Lie algebra, representation, current Heisenberg Hom-Lie algebra, derivation, cohomology, extension
In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal dimension of current Heisenberg Hom-Lie algebras. Moreover derivations, including generalized derivations, and centroids are studied. Furthermore, cohomology and extensions of current Hom-Lie algebras are also considered.