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

[摘要] We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to sl(m vertical bar 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 sl(2 vertical bar 1) this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum sl(m vertical bar n) leads to 3-manifold invariants and more generally ETQFTs. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Super quantum groups;Modified traces;Witten-Reshetikhin-Turaev invariants