Hopf Algebras in General and in Combinatorial Physics: a practical introduction

TL;DR

This tutorial provides an accessible introduction to Hopf algebras, illustrating their structures with examples from combinatorics and quantum physics, emphasizing their natural emergence in these fields.

Contribution

It offers a practical, example-driven introduction to Hopf algebras, connecting abstract theory with applications in physics and combinatorics.

Findings

Hopf algebra axioms arise naturally in quantum physics

The tutorial includes exercises from physics to deepen understanding

Examples demonstrate the relevance of Hopf algebras in combinatorics

Abstract

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced.