Quantum symmetries of faces models and the double triangle algebra

TL;DR

This paper explores the quantum symmetries of face models in statistical mechanics, revealing that their symmetry operators form a weak *-Hopf algebra equivalent to the Ocneanu double triangle algebra.

Contribution

It establishes a connection between symmetries of face models and the structure of the Ocneanu double triangle algebra, advancing understanding of quantum symmetries in integrable models.

Findings

Symmetry operators form a weak *-Hopf algebra.

The algebra is isomorphic to the Ocneanu double triangle algebra.

Provides a new algebraic framework for face model symmetries.

Abstract

Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra.