Graph Quantum Groups

TL;DR

This paper introduces graph quantum groups, a novel mathematical structure combining graph-associated algebras with Hopf algebra properties, and demonstrates their properties through examples.

Contribution

It defines the concept of graph quantum groups, integrating graph-based algebras with Hopf algebra structures, and shows how string operators become intertwiners.

Findings

Definition of graph quantum groups

Examples illustrating the structure

Connection to Ocneanu's string operators

Abstract

We define a new mathematical structure ( graph quantum group) which combines the tower of algebras associated with a graph ${\cal G}$ and the structure of a Hopf algebra {\cal A}. In this structure Ocneanu's string operators become Hopf algebra intertwiners. We present some examples of graph quantum groups.