Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups
arXiv:1812.10685 · doi:10.2140/agt.2020.20.3377
Abstract
We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for the construction of 1+1+1-TQFTs extending CGP invariants, which are non-semisimple quantum invariants of closed 3-manifolds decorated with ribbon graphs and cohomology classes. When we consider the zero cohomology class, these quantum invariants are shown to coincide with the renormalized Hennings invariants coming from the corresponding small quantum groups.
arXiv comment33 pages
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Cited by in corpus (12)
- 3-Dimensional TQFTs From Non-Semisimple Modular Categories
- On ribbon categories for singlet vertex algebras
- Non-Semisimple Extended Topological Quantum Field Theories
- Modular Categories and TQFTs Beyond Semisimplicity
- Modified graded Hennings invariants from unrolled quantum groups and modified integral
- Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
- Extended TQFTs From Non-Semisimple Modular Categories
- Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
- Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
- Homological Construction of Quantum Representations of Mapping Class Groups
- Kerler-Lyubashenko Functors on 4-Dimensional 2-Handlebodies
- Stated skein algebras and their representations