Modified graded Hennings invariants from unrolled quantum groups and modified integral

Abstract

The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$. We generalize this fact to the context of unrolled quantum groups and construct the associated topological ribbon Hopf algebras. Then we use such an algebra, the discrete Fourier transforms, a symmetrized graded integral and a modified trace to define a modified graded Hennings invariant. Finally, we use the notion of a modified integral to extend this invariant to empty manifolds and show that it recovers the CGP-invariant.

arXiv comment54 pages, 42 figures

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Cited by in corpus (4)

• Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
• Homological Construction of Quantum Representations of Mapping Class Groups
• Refined Bobtcheva-Messia Invariants of 4-Dimensional 2-Handlebodies
• Hennings TQFTs for Cobordisms Decorated With Cohomology Classes