Hecke Algebras, Modular Categories and 3-manifolds Quantum Invariants

Hecke Algebras , Modular Categories and 3 - Manifolds Quantum Invariantschristian

Face Algebras and Unitarity of Su(n)l-tqft

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 Uq(slN ) 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.

S-structures for K-linear Categories and the Definition of a Modular Functor

Motivation and background. Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras [17] [22], monoidal categories with additional structure [24], and modular functors [14] [23]. These constructions are closely related. Here we take a unifying categorical appro...

Quantum Invariants of 3-manifolds: Integrality, Splitting, and Perturbative Expansion

We consider quantum invariants of 3-manifolds associated with arbitrary simple Lie algebras. Using the symmetry principle we show how to decompose the quantum invariant as the product of two invariants, one of them is the invariant corresponding to the projective group. We then show that the projective quantum invariant is always an algebraic integer, if the quantum parameter is a prime root of...

Coribbon Hopf (face) Algebras Generated by Lattice Models

By studying “points of the underlying quantum groups”of coquasitriangular Hopf (face) algebras, we construct ribbon categories for each lattice models without spectral parameter of both vertex and face type. Also, we give a classification of the braiding and the ribbon structure on quantized classical groups and modular tensor categories closely related to quantum SU(N)Linvariants of 3-manifolds.