Simple physical applications of a groupoid structure

TL;DR

This paper explores groupoid structures inspired by quantum mechanics, focusing on cross product constructions and analyzing formal aspects of Hopf algebras.

Contribution

It introduces new cross product constructions on groupoids and critically examines foundational issues in Hopf algebra structures.

Findings

Developed new cross product constructions for groupoids

Provided critical insights into Hopf algebra formalism

Linked groupoid structures to quantum mechanics considerations

Abstract

Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.