Maximality of correspondence representations

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Abstract

In this paper, we fully characterize maximal representations of a C*-correspondence, thereby strengthening several earlier results. We demonstrate the maximality criteria through 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 Dor-On. Furthermore, we identify several classes of correspondences for which the hyperrigidity conjecture holds.

Original languageEnglish
Article number110097
JournalAdvances in Mathematics
Volume462
DOIs
StatePublished - Feb 2025

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

  • C*-correspondence
  • Choquet boundary
  • Cuntz-Pimsner algebra
  • Dilation
  • Hyperrigidity
  • Unique extension property

ASJC Scopus subject areas

  • General Mathematics

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