Modified graded Hennings invariants from unrolled quantum groups and modified integral
Autor: | Bertrand Patureau-Mirand, Ngoc Phu Ha, Nathan Geer |
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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: |
Pure mathematics
Trace (linear algebra) Topological ribbon Hopf algebra [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Context (language use) 01 natural sciences Computer Science::Digital Libraries Mathematics - Geometric Topology Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences Lie algebra Ribbon FOS: Mathematics Quantum Algebra (math.QA) Hennings type invariant 0101 mathematics Invariant (mathematics) Mathematics Algebra and Number Theory Modified integral 010308 nuclear & particles physics Quantum group 010102 general mathematics Geometric Topology (math.GT) Hopf algebra Mathematics::Geometric Topology 17B37 Discrete Fourier transform Cohomology 57M27 57M27 57M27 17B37 Unrolled quantum group |
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 |
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