Exceptional quantum subgroups for the rank two Lie algebras B2 and G2

R. Coquereaux (1, 2, 3) , R. Rais (2, 3) , E. H. Tahri (4)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332
4 Université Mohammed Premier [Oujda]

Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated algebras of quantum symmetries and discover or recover, as a by-product, the graphs describing exceptional quantum subgroups of type B2 or G2 which encode their module structure over the associated fusion category. Global dimensions are given.

Mots clés: conformal field theories; quantum symmetries; modular invariance; module-categories; conformal field theories.

Domaines: Algèbres quantiques [math.QA]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

R. Coquereaux, R. Rais, E. H. Tahri. Exceptional quantum subgroups for the rank two Lie algebras B2 and G2. Journal of Mathematical Physics, 2010, 51 (9), pp.092302. ⟨10.1063/1.3476319⟩. ⟨hal-00451945⟩