University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003120220701On hyperactions and Lie hypergroup127140173710.22098/jfga.2022.10397.1060ENNeda EbrahimiDepartment of Pure Mathematics, Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman & Mahani Mathematical Reaserch
Center, 7616914111, Kerman, Iran.Tayebeh WaezizadehDepartment of Pure Mathematics, Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman & Mahani Mathematical Reaserch
Center, 7616914111, Kerman, Iran.Journal Article20220220Using 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.https://jfga.uma.ac.ir/article_1737_36770bf1a9dc5cc022cdf7334ddea58d.pdf