Modified graded Hennings invariants from unrolled quantum groups and modified integral

Autor: Bertrand Patureau-Mirand, Ngoc Phu Ha, Nathan Geer
Přispěvatelé: Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: J.Pure Appl.Algebra
J.Pure Appl.Algebra, 2022, 226, pp.106815. ⟨10.1016/j.jpaa.2021.106815⟩
DOI: 10.1016/j.jpaa.2021.106815⟩
Popis: 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.
54 pages, 42 figures
Databáze: OpenAIRE