Logarithmic knot invariants arising from restricted quantum groups

TL;DR

This paper develops new knot invariants based on the radical parts of projective modules from restricted quantum groups, linking them to colored Alexander invariants, and expanding the understanding of quantum knot invariants.

Contribution

It introduces a novel construction of knot invariants using the radical parts of projective modules in restricted quantum groups, establishing a connection to colored Alexander invariants.

Findings

Knot invariants derived from restricted quantum groups' projective modules.

Established a relation between these invariants and colored Alexander invariants.

Enhanced the framework for quantum knot invariants.

Abstract

We construct knot invariants from the radical part of projective modules of restricted quantum groups. We also show a relation between these invariants and the colored Alexander invariants.