Study On Hom-Lie Algebras Over A Field Of Prime Characteristic

In this paper,we mainly consider Hom-Lie algebras over a field of prime characteristic.First,Hom-universal enveloping algebras of Hom-Lie algebras are investigated.In particular,by endowing sl(n,F)with the structure of a Hom-Lie algebra,the Hom-PBW type basis of Hom-Lie algebra sl(n,F)is constructed.Furthermore,in the restricted case,the restricted Hom-universal enveloping algebra of restricted Hom-Lie algebra sl(n,F)is studied.Finally,Hom-p-envelops and Hom-universal p-envelops of Hom-Lie algebras are discussed.