Quantum groups and braid groups as fundamental symmetries

TL;DR

This paper explores the application of quantum groups and braid groups as fundamental symmetries in the Standard Model, highlighting recent results on $SU_q(3)$ and connecting algebraic and braided descriptions of elementary particles.

Contribution

It introduces a novel connection between quantum group symmetries and braided matter descriptions, advancing the understanding of Standard Model symmetries.

Findings

Quantum group $SU_q(3)$ as a flavour symmetry

Connection between division algebra and braided particle descriptions

Recent results on quantum groups in particle physics

Abstract

The role of quantum groups and braid groups in the description of Standard Model particles is discussed. Some recent results on the use of the quantum group $SU_q(3)$ as a flavour symmetry are reviewed and a connection between two descriptions of Standard Model symmetries, one based on the normed division algebras and the other describing elementary matter as braided objects, is presented.