Classification of irreversible and reversible Pimsner operator algebras

Adam Dor-On, Søren Eilers, Shirly Geffen

Research output: Contribution to journalArticlepeer-review


Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought sincetheir emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and -algebras with additional -algebraic structure. Our approach naturally applies to algebras arising from -correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

Original languageEnglish
Pages (from-to)2510-2535
Number of pages26
JournalCompositio Mathematica
StateAccepted/In press - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 The Author(s).


  • K-theory
  • Pimsner algebras
  • classification
  • graph algebras
  • non-commutative boundary
  • reconstruction
  • rigidity
  • tensor algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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