Reconstruction of tensor categories of type G₂

2025/10/10 by Martirosyan, Lilit, Wenzl, Hans · 2 citations
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.09922

Abstract

We prove that any non-symmetric ribbon tensor category C with the fusion rules of the compact group of type G₂ needs to be equivalent to the representation category of the corresponding Drinfeld-Jimbo quantum group for q not a root of unity. We also prove an analogous result for the corresponding finite fusion tensor categories.

Citations

• Simple B₄ representations associated to cyclotomic Hecke algebras
• Near-integral fusion
• Auto-equivalences of the modular tensor categories of type A, B, C and G
• Braid Rigidity for Path Algebras
• Categories generated by a trivalent vertex
• A cubic defining algebra for the Links-Gould polynomial
• The cubic Hecke algebra on at most 5 strands
• Quantum Groups at Roots of Unity and Modularity
• Nilpotence, radicaux et structures mono"ıdales
• The automorphisms of affine fusion rings
• Representations of the braid group B₃ and of SL(2,Z)
• Quantum Invariants of Knots and 3-Manifolds

Cited by

• A characterization of the Delannoy category by Adams operations
• Simple B₄ representations associated to cyclotomic Hecke algebras

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• Quantum G₂ categories have property (T)
• On braided tensor categories
• Quantum groups and ribbon G-categories
• The representation category of the Woronowicz quantum group S_mu U(d) as a braided tensor C*-category
• On the center of near-group fusion category of type ℤ₃+6