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Article Dans Une Revue Journal of Algebra Année : 2021

Renormalized Witten-Reshetikhin-Turaev invariants and m-traces associated to the special linear Lie superalgebra

Relative (pre)-modular categories from special linear Lie superalgebras

Résumé

We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to $\mathfrak{sl}(m|n)$ at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended Topological Quantum Field Theories. The second m-trace is on the ideal of perturbative typical modules. We consider the quotient with respect to negligible morphisms coming from this m-trace and show that in the case of $\mathfrak{sl}(2|1)$ this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum $\mathfrak{sl}(m|n)$ leads to 3-manifold invariants and more generally ETQFTs.

Dates et versions

hal-02992272 , version 1 (06-11-2020)

Identifiants

Citer

Cristina Ana-Maria Anghel, Nathan Geer, Bertrand Patureau-Mirand. Renormalized Witten-Reshetikhin-Turaev invariants and m-traces associated to the special linear Lie superalgebra. Journal of Algebra, 2021, 586, pp.479-525. ⟨10.1016/j.jalgebra.2021.06.035⟩. ⟨hal-02992272⟩
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