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

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.