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Iterated Function Systems and Permutation Representations of the Cuntz Algebra
Ola Bratteli, University of Oslo, Norway, and Palle E. T. Jorgensen, University of Iowa, Iowa City, IA

Memoirs of the American Mathematical Society
1999; 89 pp; softcover
Volume: 139
ISBN-10: 0-8218-0962-8
ISBN-13: 978-0-8218-0962-4
List Price: US$49
Individual Members: US$29.40
Institutional Members: US$39.20
Order Code: MEMO/139/663
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Graduate students and research mathematicians working in functional analysis.

Table of Contents

  • Introduction
  • Permutative representations of \(\mathcal O_N\)
  • Monomial representations and integers modulo \(N\)
  • Cycles of irreducible \(\mathcal O_N\) representations and their atoms of UHF\(_N\) representations
  • Relations of finite type and sub-Cuntz states
  • The shift representation
  • The universal permutative multiplicity-free representation
  • Some specific examples of the cycle and atom structure: The mod \(N\) case
  • Some specific examples of the cycle and atom structure: The mod \(\mathbf N\) case
  • The general mod \(\mathbf N\) situation
  • Concluding remarks
  • Bibliography
  • List of symbols
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