Tensor categories attached to double groupoids
Copyright policy )Tensor categories attached to double groupoids
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.
Revised version to appear in Adv. Math., 45 pages. Added examples where the square of the antipode is not the identity, necessary and sufficient conditions for the representation category to be fusion, and the computation of quantum and Frobenius-Perron dimensions of simple representations
- Universidad Nacional de Córdoba (UNC) Argentina
- National Scientific and Technical Research Council Argentina
- National University of Córdoba Argentina
Mathematics(all), 18D05, Tensor category, Double groupoid, Groupoids (i.e. small categories in which all morphisms are isomorphisms), Hopf algebras (associative rings and algebras), 20L05, Double categories, \(2\)-categories, bicategories and generalizations, 16W30; 20L05; 18D05; 18B40, 18B40, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), double groupoids, weak Hopf algebras, Weak Hopfalgebra, tensor categories, 16W30, Groupoids, semigroupoids, semigroups, groups (viewed as categories)
Mathematics(all), 18D05, Tensor category, Double groupoid, Groupoids (i.e. small categories in which all morphisms are isomorphisms), Hopf algebras (associative rings and algebras), 20L05, Double categories, \(2\)-categories, bicategories and generalizations, 16W30; 20L05; 18D05; 18B40, 18B40, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), double groupoids, weak Hopf algebras, Weak Hopfalgebra, tensor categories, 16W30, Groupoids, semigroupoids, semigroups, groups (viewed as categories)
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