Frontiers of Mathematics in China >
Extensions of n-Hom Lie algebras
Received date: 23 Jan 2014
Accepted date: 26 Mar 2014
Published date: 01 Apr 2015
Copyright
n-Hom Lie algebras are twisted by n-Lie algebras by means of twisting maps. n-Hom Lie algebras have close relationships with statistical mechanics and mathematical physics. The paper main concerns structures and representations of n-Hom Lie algebras. The concept of nρ-cocycle for an n-Hom Lie algebra (G, [,… , ], α) related to a G-module (V, ρ, β) is proposed, and a sufficient condition for the existence of the dual representation of an n-Hom Lie algebra is provided. From a G-module (V, ρ, β) and an nρ-cocycle θ, an n-Hom Lie algebra (Tθ(V ), [, … , ]θ, γ) is constructed on the vector space Tθ(V ) = G⊕V, which is called the Tθ-extension of an n-Hom Lie algebra (G, [, … , ], α) by the G-module (V, ρ, β).
Key words: n-Hom Lie algebra; representation; extension; nρ-cocycle
Ruipu BAI , Ying LI . Extensions of n-Hom Lie algebras[J]. Frontiers of Mathematics in China, 2015 , 10(3) : 511 -522 . DOI: 10.1007/s11464-014-0372-8
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