Face algebras and unitarity of SU(N)_L-TQFT

Abstract

Using face algebras (i.e. algebras of L-operators of IRF models), we construct modular tensor categories with positive definite inner product, whose fusion rules and S-matrices are the same as (or slightly different from) those obtained by $U_q({\mathfrak{sl}}_N)$ at roots of unity. Also we obtain state-sums of ABF models on framed links which give quantum SU(2)-invariants of corresponding 3-manifolds.

AMS-LaTeX, 36 pages, to appear in Commun. Math. Phys

References in corpus (1)

• A Coassociative C*-Quantum Group with Non-Integral Dimensions

Cited by in corpus (8)

• A canonical Tannaka duality for finite seimisimple tensor categories
• Partial compact quantum groups
• A proof of the Brown--Goodearl Conjecture for weak Hopf algebras
• Algebraic structures in comodule categories over weak bialgebras
• C*-algebraic partial compact quantum groups
• Coribbon Hopf (face) algebras generated by lattice models
• Braided autoequivalences and quantum commutative bi-Galois objects
• Symmetries of algebras captured by actions of weak Hopf algebras