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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
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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$46
Individual Members: US$27.60
Institutional Members: US$36.80
Order Code: MEMO/139/663
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Readership

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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