On hyperactions and Lie hypergroup

Using the action of a Lie group on a hypergroup, the notion of Lie hypergroup is defined. It is proved that tangent space of a Lie hypergroup is a hypergroup and that a differentiable map between two Lie hypergroup is good homomorphism if and only if its differential map is a good homomorphism. The action of a hypergroup on a set is defined. Using this notion, hypergroup bundle is introduced and some of its basic properties are investigated. In addition, some results on qutient hypergroups are given.

Keywords:

Hypergroup , Action , Quotient Space , Sub Hypergroup , Hypergroup Bundle