Extensions of n-Hom Lie algebras  

作　　者：Ruipu BAI Ying LI 

机构地区：[1]College of Mathematics and Computer Science, Hebei University, Baoding 071002, China

出　　处：《Frontiers of Mathematics in China》2015年第3期511-522,共12页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant No. 11371245） and the Natural Science Foundation of Hebei Province, China （Grant No. A2014201006）.

摘　　要：n-Hom Lie algebras are twisted by n-Lie algebras by means of twisting maps. n-Horn Lie algebras have close relationships with statistical mechanics and mathematical physics. The paper main concerns structures and representations of n-Horn 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-Horn 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-Horn Lie algebra （G, [,..., ], α） by the G-module （V, ρ,β）.n-Hom Lie algebras are twisted by n-Lie algebras by means of twisting maps. n-Horn Lie algebras have close relationships with statistical mechanics and mathematical physics. The paper main concerns structures and representations of n-Horn 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-Horn 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-Horn Lie algebra （G, [,..., ], α） by the G-module （V, ρ,β）.

关 键 词：n-Horn Lie algebra REPRESENTATION EXTENSION np-cocycle 

分 类 号：O152.5[理学—数学] O411.1[理学—基础数学]