On the capablility of Hom-Lie algebras

Abstract

A Hom-Lie algebra $(L,{\alpha }_L)$ is said to be capable if there exists a Hom-Lie algebra $(H,{\alpha }_H)$ such that $L\cong H/Z(H)$. 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.

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