Hypergroups and polygroups in diffeology

Abstract

We introduce diffeological algebraic hyperstructures such as diffeological hypergroups and diffeological polygroups, which are generalizations of diffeological groups. After providing some examples of these notions, we investigate the relationships between diffeological hypergroups and diffeological groups. It is proved that there is an equivalence of categories between subductions over diffeological groups and diffeological complete hypergroups. We finally show how every diffeological polygroup is a subpolygroup of a diffeological poly-monoid of hyper-diffeomorphisms.

Communicated by J. L. Gomez Pardo

Keywords:

• Algebraic hyperstructures
• diffeological groups
• diffeological hypergroups
• diffeological polygroups
• diffeology
• hyper-diffeomorphisms

2010 Mathematics Subject Classification:

• 20N20
• 57P99