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  • Ergodic Theory and Dynamical Systems, Volume 15, Issue 5
  • October 1995, pp. 993-1003

Some ergodic properties for infinite graphs associated with subfactors

  • Sorin Popa (a1)
  • DOI:
  • Published online: 14 October 2010

We prove that the restriction of the graph of a subfactor, ΓN,M, to an infinite subset of vertices with finite boundary has the same norm as ΓN,W. In particular, if N φ M is extremal with [M : N] > 4 and ΓN,M has an A∞, tail then ΓN, M = A∞.

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[Hi] F. Hiai . Minimizing indices of conditional expectations onto a subfactor. Publ. RIMS 24 (1988), 673678.

[Iz] M. Izumi . Applications of fusion rules to classification of subfactors. Publ. RIMS Kyoto Univ. 27 (1991), 953994.

[J] V. F. R. Jones . Index for subfactors. Invent. Math. 72 (1983), 125.

[L] R. Longo . Minimal index and braided subfactors. J Fund. Analysis 109 (1991), 98112.

[PiPo2] M. Pimsner and S. Popa . Iterating the basic construction. Trans. Amer. Math. Soc. 310 (1988), 127133.

[PiPo3] M. Pimsner and S. Popa . Finite dimensional approximation for pairs of algebras and obstructions for the index. J. Fund. Analysis 98 (1991), 270291.

[Pol] S. Popa . Classification of subfactors: Reduction to commuting squares. Invent. Math. 101 (1990), 1943.

[PoS] S. Popa . On a problem of R. V. Kadison on maximal Abelian *-subalgebras in factors. Invent. Math. 65 (1981), 269281.

[SV] S. Sunder and A. Vijayavagan . On the non-occurence of the coxeter graphs E7, D2n+1 as principal graphs of an inclusion of II1 factors. Pac. J. Math. 161 (1993), 185200.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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