Derivations and Spectral Triples on Quantum Domains II: Quantum Annulus

TL;DR

This paper explores spectral triples on the quantum annulus, focusing on unbounded derivations and their implementation via operators with compact parametrices, crucial for defining spectral triples.

Contribution

It investigates the conditions under which invariant and covariant derivations on the quantum annulus can be implemented by operators with compact parametrices, advancing the understanding of spectral triples on quantum domains.

Findings

Identifies conditions for derivations to have compact parametrices

Analyzes the structure of spectral triples on the quantum annulus

Provides criteria for implementing derivations with suitable operators

Abstract

Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we investigate whether such derivations can be implemented by operators with compact parametrices, a necessary condition in the definition of a spectral triple.