Topological invariants from quantum group $\mathcal{U}_{\xi}\mathfrak{sl}(2|1)$ at roots of unity

TL;DR

This paper develops new topological invariants for links and 3-manifolds using quantum groups related to the Lie superalgebra sl(2|1) at roots of unity, leveraging advanced categorical techniques.

Contribution

It introduces a novel construction of topological invariants from sl(2|1) quantum groups at roots of unity using modified trace and G-modular categories.

Findings

Constructed link invariants from sl(2|1) quantum groups at roots of unity.

Developed 3-manifold invariants based on these quantum groups.

Utilized the framework of nilpotent representations and modified traces.

Abstract

In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. This construction based on nilpotent irreducible finite dimensional representations of quantum group $\mathcal{U}_{\xi}\mathfrak{sl}(2|1)$ where $\xi$ is a root of unity of odd order. These constructions use the notion of modified trace and relative $\mathit{G}$-modular category.