On coset $n$-valued topological groups on $S^3$ and $\mathbb{R}P^3$

TL;DR

This paper classifies all coset n-valued topological groups on the 3-sphere and real projective 3-space derived from compact Lie groups and their automorphisms.

Contribution

It provides a complete classification of coset n-valued topological groups on $S^3$ and $\,\mathbb{R}P^3$ based on compact Lie groups and automorphisms.

Findings

All such groups are classified explicitly.

The classification involves groups from Sp(1) and SO(3).

Automorphisms play a key role in the structure.

Abstract

We obtain all coset $n$-valued topological groups on $S^3$ and $\mathbb{R}P^3$, arising from compact Lie groups Sp(1) and SO(3) and there finite groups of automorphisms.