## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 10, Number 1 (2006), 49-75.

### Quantum symmetries of face models and the double triangle algebra

#### 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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 10, Number 1 (2006), 49-75.

**Dates**

First available in Project Euclid: 30 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1154236238

**Mathematical Reviews number (MathSciNet)**

MR2222222

**Zentralblatt MATH identifier**

1130.81038

**Subjects**

Primary: 81T40: Two-dimensional field theories, conformal field theories, etc.

Secondary: 16W30 81R05: Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]

#### Citation

Trinchero, Roberto. Quantum symmetries of face models and the double triangle algebra. Adv. Theor. Math. Phys. 10 (2006), no. 1, 49--75. https://projecteuclid.org/euclid.atmp/1154236238