Maximality of correspondence representations

TL;DR

This paper characterizes maximal representations of C*-correspondences, strengthening prior results, and explores noncommutative boundaries and hyperrigidity conjecture with new examples and counterexamples.

Contribution

It provides a complete characterization of maximal C*-correspondence representations and discusses noncommutative boundaries and hyperrigidity, extending previous work with new examples.

Findings

Complete characterization of maximal representations

Counterexamples to Arveson's hyperrigidity conjecture

Description of noncommutative Choquet boundary

Abstract

In this paper, we fully characterize maximal representations of a C*-correspondence. This strengthens several earlier results. We demonstrate the criterion with diverse examples. We also describe the noncommutative Choquet boundary and provide additional counterexamples to Arveson's hyperrigidity conjecture following the counterexample recently found by the author and Adam Dor-On.