A Hermitian TQFT from a non-semisimple category of quantum $${\mathfrak {sl}(2)}$$-modules

Abstract

We endow a non-semisimple category of modules of unrolled quantum \({\mathfrak {sl}(2)}\) with a Hermitian structure. We also prove that the CGP 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.