HNN-extension of involutive multiplicative Hom-Lie algebras

Abstract

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 Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.

Operadic approach to HNN-extensions of Leibniz algebras

“…For a group G with an isomorphism φ between two of its subgroups A and B, H is an extension of G with an element t ∈ H, such that t −1 at = φ(a) for every a ∈ A. The group H is presented by H = G, t | t −1 at = φ(a), a ∈ A and it implies that G is embedded in H. The concept of HNN-extension was constructed for (restricted) Lie algebras in independent works by Lichtman and Shirvani [4] and Wasserman [19], and it has recently been extended to generalized versions of Lie algebras, namely, Leibniz algebras, Lie superalgebras and Hom-setting of Lie algebras in [10], [11] and [18], respectively. As an application of HNN-extensions, Wasserman in [19] obtained some analogous results to group theory and proved that Markov properties of finitely presented Lie algebras are undecidable.…”