Some Properties Of Restricted Hom-Lie Algebras

The hom-algebra structures arose first in quasi-deformation of Lie algebras of vector fields.Discrete modifications of vector fields via twisted derivations lead to hom-Lie and quasi-hom-Lie structures in which the Jacobi condition is twisted by a linear map,called the hom-Jacobi identity.Now,hom-Lie algebra are widely studied because of the dual need of physics and Lie algebras.The restricted Lie algebras play a predominant role in the study of modular Lie algebras.The p-mappings in Lie algebras have the same basic features as the mapping x ? xpof a given associative F-algebra.Recently,the equivalent definition of restricted hom-Lie algebras have been given.On the basis of that we mainly put hom-Lie p-subalgebra and semisimple elements into restricted hom-Lie algebras in this paper.In particular,torus and Cartan decomposition of the restricted hom-Lie algebras are investigated in details.