# Derivations and Spectral Triples on Quantum Domains I: Quantum Disk

## TL;DR

This paper investigates unbounded derivations on the quantum disk to determine if they can generate spectral triples, focusing on their properties related to operators with compact parametrices.

## Contribution

It provides an analysis of invariant and covariant derivations on the quantum disk and addresses whether these derivations originate from operators suitable for spectral triples.

## Key findings

- Characterization of derivations on the quantum disk
- Conditions under which derivations come from operators with compact parametrices
- Implications for constructing spectral triples on quantum domains

## Abstract

We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.