Relative Cuntz--Pimsner algebras: classification of gauge-equivariant representations: a simple and complete picture

TL;DR

This paper provides a straightforward and comprehensive framework for classifying relative Cuntz--Pimsner algebras and gauge-equivariant representations through an intuitive parameterization involving kernel--covariance pairs.

Contribution

It introduces a simple and complete classification method for relative Cuntz--Pimsner algebras based on kernel--covariance pairs, enhancing understanding of their structure.

Findings

Unified classification framework for relative Cuntz--Pimsner algebras

Parametrization by kernel--covariance pairs simplifies analysis

Clarifies the structure of gauge-equivariant representations

Abstract

We give a simple and complete picture on the classification of relative Cuntz--Pimsner algebras (and so also of gauge-equivariant representations) using their intuitive parametrisation by kernel--covariance pairs.