On the capability of Hom-Lie algebras

Abstract

A Hom-Lie algebra (L, αL) is said to be capable if there exists a Hom-Lie algebra (H, αH) such that L – H/Z(H). We obtain a characterisation of capable Hom-Lie algebras involving its epicentre and we use this theory to further study the six-term exact sequence in homology and to obtain a Hopf-type formulae of the second homology of perfect Hom-Lie algebras.