A Non-abelian Tensor Product of Hom–Lie Algebras

Non-abelian tensor product of Hom–Lie algebras is constructed and studied. This tensor product is used to describe universal ($$\alpha $$ α )-central extensions of Hom–Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition.