On invariants of graphs related to quantum $\mathfrak{sl}(2)$ at roots of unity

TL;DR

This paper develops a method to define invariants for multi-component graphs colored by certain quantum group representations with zero quantum dimensions, extending previous invariants to more complex graph structures.

Contribution

It introduces a new approach to define invariants of graphs with multiple components and zero quantum dimension colorings related to quantum sl(2) at roots of unity.

Findings

Defined invariants for multi-component graphs with zero quantum dimension colorings.

Extended the applicability of quantum sl(2) invariants to more complex graph configurations.

Provided a framework for analyzing invariants in the context of quantum groups at roots of unity.

Abstract

We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.