Metrics On The Quantum Heisenberg Manifold

TL;DR

This paper constructs Lip norms on the order unit space of smooth elements in the quantum Heisenberg manifold, contributing to the understanding of quantum metric spaces.

Contribution

It introduces Lip norms on the selfadjoint part of the smooth subalgebra of the quantum Heisenberg manifold, advancing quantum metric space theory.

Findings

Established Lip norms on the quantum Heisenberg manifold

Enhanced the framework of quantum metric spaces

Provided tools for analyzing quantum geometric structures

Abstract

Compact quantum metric spaces are order unit spaces along with a Lip norm. On the order unit space of the selfadjoint elements of the dense subalgebra of smooth elements in the quantum Heisenberg manifold we construct Lip norms.