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# Advances in Theoretical and Mathematical Physics

## Volume 10 (2006)

### Number 1

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

Pages: 49 – 75

DOI: http://dx.doi.org/10.4310/ATMP.2006.v10.n1.a3

#### Author

#### 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.

#### 2010 Mathematics Subject Classification

Primary 81T40. Secondary 81R05.