Advances in Theoretical and Mathematical Physics

On quantum symmetries of ADE graphs

Robert Coquereaux and Roberto Trinchero

Abstract

The double triangle algebra (DTA) associated to an ADE graph is considered. A description of its bialgebra structure based on a reconstruction approach is given. This approach takes as initial data the representation theory of the DTA as given by Ocneanu's cell calculus. It is also proved that the resulting DTA has the structure of a weak *-Hopf algebra. As an illustrative example, the case of the graph A3 isdescribed in detail.

Article information

Source
Adv. Theor. Math. Phys., Volume 8, Number 1 (2004), 189-216.

Dates
First available in Project Euclid: 2 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1091475317

Mathematical Reviews number (MathSciNet)
MR2086679

Zentralblatt MATH identifier
1082.81045

Citation

Coquereaux, Robert; Trinchero, Roberto. On quantum symmetries of ADE graphs. Adv. Theor. Math. Phys. 8 (2004), no. 1, 189--216. https://projecteuclid.org/euclid.atmp/1091475317


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