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Iterated function systems and permutation representations of the Cuntz algebra

About this Title

Ola Bratteli and Palle E. T. Jorgensen

Publication: Memoirs of the American Mathematical Society
Publication Year 1999: Volume 139, Number 663
ISBNs: 978-0-8218-0962-4 (print); 978-1-4704-0252-5 (online)
MathSciNet review: 1469149
MSC: Primary 46Lxx; Secondary 11B85, 22D25, 39B12, 42C15, 47D25

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Table of Contents


  • 1. Introduction
  • 2. Permutative representations of $\mathcal {O}_N$
  • 3. Monomial representations and integers modulo $N$
  • 4. Cycles of irreducible $\mathcal {O}_N$ representations and their atoms of $\mathrm {UHF}_N$ representations
  • 5. Relations of finite type and sub-Cuntz states
  • 6. The shift representation
  • 7. The universal permutative multiplicity-free representation
  • 8. Some specific examples of the cycle and atom structure: The mod $N$ case
  • 9. Some specific examples of the cycle and atom structure: The mod N case
  • 10. The general mod N situation
  • 11. Concluding remarks