HNN-extension of involutive multiplicative Hom-Lie algebras

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincar'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.