# Coverings of Quantum Groups

## TL;DR

This paper explores the noncommutative generalization of coverings of topological groups, focusing on quantum groups, and investigates how these coverings differ from classical cases in structure and properties.

## Contribution

It introduces a framework for understanding coverings of quantum groups, highlighting their weaker structural conditions compared to classical topological group coverings.

## Key findings

- Coverings of quantum groups do not naturally inherit the quantum group structure.
- A weaker condition than classical coverings applies to quantum group coverings.
- The study advances the understanding of noncommutative topology and quantum algebra structures.

## Abstract

It is known that any covering space of a topological group has the natural structure of a topological group. This article discusses a noncommutative generalization of this fact. A noncommutative generalization of the topological group is a quantum group. Also there is a noncommutative generalization of a covering. The combination of these algebraic constructions yields a motive to research the generalization of coverings of topological groups. In contrary to a topological group a covering space of a quantum group does not have the natural structure of the quantum group. However a covering space of a quantum group satisfies to a condition which is weaker than the condition of a covering space of a topological group.