A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules

Abstract

We endow a non-semisimple category of modules of unrolled quantum sl(2) with a Hermitian structure. We also prove that the TQFT constructed in arXiv:1202.3553 using this category is Hermitian. This gives rise to projective representations of the mapping class group in the group of indefinite unitary matrices.

18 pages

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs

Cited by in corpus (3)

• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
• A non-semisimple non-invertible symmetry