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

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

1999-04-16

arxiv.org/abs/math/9904082v1

Commun.Math.Phys. 203 (1999) 211-247

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s002200050610

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 $U_q (\frak{sl}_{N})$ 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.

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