Hom-Lie Groups And Hom-Lie Algebras

This thesis mainly studies the relation between Hom-Lie algebras and Hom-Lie groups by introducing the concept of Hom-Lie groups.In Chapter 1,we introduce the background and its recent development and analyzes the motivations and the main results of this thesis.In Chapter 2,we recall some basic definitions and results concerning Lie groups,Lie algebras and Hom-Lie algebras.In Chapter 3,we define the notion of a Hom-Lie groups with some useful examples.If(,?,0)_?,?)is a Hom-Lie groups,then we show that the space of left-invariant sections of the pullback bundle?!has a Hom-Lie algebras structure.Consequently,we deduce a Hom-Lie algebras structure on the fibre of pullback bundle?!at0)_?.In this way,we associate a Hom-Lie algebras(g!,[·,·]_g!,_g!)to the Hom-Lie groups(,?,0)?,?),where g!:=?!0)_?.Finally,We also show that every regular Hom-Lie algebras is integrable.