# Derivations and Reflection Positivity on the Quantum Cylinder

## TL;DR

This paper explores the structure of unbounded derivations in the quantum cylinder and establishes a noncommutative reflection positivity principle for Laplace-type operators, extending classical ideas to quantum settings.

## Contribution

It introduces a noncommutative reflection positivity framework for Laplace operators on quantum cylinders, generalizing classical reflection positivity results.

## Key findings

- Established a noncommutative reflection positivity for Laplace-type operators
- Described the structure of unbounded derivations in the quantum cylinder
- Extended classical reflection positivity concepts to noncommutative geometry

## Abstract

We describe the general structure of unbounded derivations in the quantum cylinder. We prove a noncommutative analog of reflection positivity for Laplace-type operators in a noncommutative cylinder following the ideas of Jaffe and Ritter proof of reflection positivity for Laplace operators on manifolds equipped with a reflection.