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Article Dans Une Revue Journal of the London Mathematical Society Année : 2024

Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups

Nathan Geer
  • Fonction : Auteur
Aaron Lauda
  • Fonction : Auteur
Joshua Sussan
  • Fonction : Auteur

Résumé

We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models.

Dates et versions

hal-03769530 , version 1 (05-09-2022)

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Citer

Nathan Geer, Aaron Lauda, Bertrand Patureau-Mirand, Joshua Sussan. Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups. Journal of the London Mathematical Society, 2024, 109 (1), ⟨10.1112/jlms.12853⟩. ⟨hal-03769530⟩
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