Structure of wrap groups of quaternion and octonion fiber bundles

TL;DR

This paper investigates the structure of wrap groups associated with fiber bundles over real, complex, quaternion, and octonion fields, including their iterated forms and smashed product constructions.

Contribution

It introduces the analysis of wrap groups over quaternion and octonion fields and explores their iterated versions and smashed product structures, advancing understanding of these algebraic objects.

Findings

Characterization of wrap groups over quaternion and octonion fields

Construction of iterated wrap groups and their smashed products

Extension of wrap group theory to non-associative algebras

Abstract

This article is devoted to the investigation of structure of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Iterated wrap groups are studied as well. Their smashed products are constructed.