# Nichols algebras that are quantum planes

## TL;DR

This paper classifies all 2-dimensional Nichols algebras with non-trivial quadratic relations, providing a comprehensive understanding of their structure as quantum planes.

## Contribution

It explicitly computes and classifies all such Nichols algebras of dimension 2 with quadratic relations, advancing the understanding of their algebraic structure.

## Key findings

- Complete classification of 2D Nichols algebras with quadratic relations
- Identification of conditions for non-trivial quadratic relations
- Contribution to the theory of quantum planes

## Abstract

We compute all Nichols algebras of rigid vector spaces of dimension 2 that admit a non-trivial quadratic relation.