# Quantum groups and noncommutative spacetimes with cosmological constant

## TL;DR

This paper reviews the construction of noncommutative (anti-)de Sitter spacetimes using quantum groups, highlighting how quantum deformation parameters relate to Planck scale and cosmological constant, bridging quantum gravity and cosmology.

## Contribution

It introduces a framework connecting quantum group deformations with noncommutative spacetimes incorporating cosmological constant effects.

## Key findings

- Quantum deformation parameter linked to Planck scale.
- Cosmological constant acts as a second geometric deformation parameter.
- Limit $\Lambda o 0$ yields noncommutative Minkowski spacetime.

## Abstract

Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter $z$ is related to a Planck scale, and the cosmological constant $\Lambda$ plays the role of a second deformation parameter of geometric nature, whose limit $\Lambda\to 0$ provides the corresponding noncommutative Minkowski spacetimes.