Operator algebras for higher rank analysis and their application to factorial languages

Adam Dor-On, Evgenios T.A. Kakariadis

Research output: Contribution to journalArticlepeer-review


We study strong compactly aligned product systems of ℤ+N over a C*-algebra A. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite). Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.

Original languageEnglish
Pages (from-to)555-613
Number of pages59
JournalJournal d'Analyse Mathematique
Issue number2
StatePublished - Jun 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


Dive into the research topics of 'Operator algebras for higher rank analysis and their application to factorial languages'. Together they form a unique fingerprint.

Cite this