On universal central extensions of Hom-Lie algebras

A Non-abelian Tensor Product of Hom–Lie Algebras

“…In this section, we complement by new results the investigation of universal central extensions of Hom-Lie algebras done in [3]. We also describe universal (α-)central extensions via Hom-Lie tensor product.…”

“…The homology of Hom-Lie algebras, generalizing the classical Chevalley-Eilenberg homology of Lie algebras, is constructed in [17,19] (see also [3]). Let us recall that…”

“…Thus, it is natural to seek for possible generalizations of known theories from Lie to Hom-Lie algebras. In this context, recently there have been several works dealing with the study of Hom-Lie structures (see [3,12,[14][15][16][17][18][19]). …”

On some properties preserved by the non-abelian tensor product of Hom-Lie algebras

“…The weak α-identity condition leads us to a broader class of examples. For instance, let (Q, α Q ) be the two-dimensional Hom-Lie algebra with basis {a 1 , a 2 }, bracket operation given by [a 1 , a 2 ] = −[a 2 , a 1 ] = a 1 and endomorphism α Q represented by the matrix 0 1 0 1 (see [1]). Then (Q, α Q ) satisfies weak α-identity condition, it does not satisfy α-identity condition and at the same time α Q is not surjective.…”

“…In this context, during the last years many papers appeared dealing with the investigations of Hom-Lie structures. Often in these investigations many non-obvious algebraic identities need to be verified and they are sufficiently nontrivial and interesting (see e. g. [1,2,3,4,10,11,13,14] and related references given there).…”