Tensor categories attached to double groupoids

Details Tensor categories attached to double groupoids Tensor categories attached to double groupoids

2004-08-03

arxiv.org/abs/math/0408045v2

Adv. Math. 200 (2006) pp. 539-583

Mathematics

Quantum Algebra

Revised version to appear in Adv. Math., 45 pages. Added examples where the square of the antipode is not the identity, necess

Scientific paper

The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. This extends previous work that appeared in math.QA/0308228. Several important classes of examples of tensor categories are shown to fit into this construction. Certain invariants such as a pivotal group-like element and quantum and Frobenius-Perron dimensions of simple objects are computed.

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