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Some ergodic properties for infinite graphs associated with subfactors

Published online by Cambridge University Press:  14 October 2010

Sorin Popa
Sorin Popa
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024-1555, USA
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Abstract

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∞.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995, pp. 993 - 1003
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

[GUJ] Goodman, F., Harpe, P. de la and Jones, V. F. R.. Coxeter graphs and towers of algebras. MSRI Publ. 14. Springer, Berlin, 1989.Google Scholar
[Ha] Haagerup, U.. Principal graphs of subfactors in the index range . In Subfactors. pp. 1–32. World Scientific, Singapore-New Jersey-Hong Kong, 1994.Google Scholar
[Hi] Hiai, F.. Minimizing indices of conditional expectations onto a subfactor. Publ. RIMS 24 (1988), 673–678.CrossRefGoogle Scholar
[Iz] Izumi, M.. Applications of fusion rules to classification of subfactors. Publ. RIMS Kyoto Univ. 27 (1991), 953–994.CrossRefGoogle Scholar
[J] Jones, V. F. R.. Index for subfactors. Invent. Math. 72 (1983), 1–25.CrossRefGoogle Scholar
[L] Longo, R.. Minimal index and braided subfactors. J Fund. Analysis 109 (1991), 98–112.CrossRefGoogle Scholar
[Oc] Ocneanu, A.. Quantized group string algebras and Galois theory for algebras. In Operator Algebras and Applications. Vol. 2. London Mathematical Society Lecture Notes Series 136 (1989), 119–172.CrossRefGoogle Scholar
[PiPol] Pimsner, M. and Popa, S.. Entropy and index for subfactors. Ann. Ec. Norm. Sup. 19 (1986), 57–106.CrossRefGoogle Scholar
[PiPo2] Pimsner, M. and Popa, S.. Iterating the basic construction. Trans. Amer. Math. Soc. 310 (1988), 127–133.CrossRefGoogle Scholar
[PiPo3] Pimsner, M. and Popa, S.. Finite dimensional approximation for pairs of algebras and obstructions for the index. J. Fund. Analysis 98 (1991), 270–291.CrossRefGoogle Scholar
[Pol] Popa, S.. Classification of subfactors: Reduction to commuting squares. Invent. Math. 101 (1990), 19–43.CrossRefGoogle Scholar
[Po2] Popa, S.. Classification of amenable subfactors of type II. Ada Math. 72(2) (1994), 352–445.Google Scholar
[Po3] Popa, S.. Approximate innerness and central freeness for subfactors: A classification result. In Subfactors. pp. 274–293. World Scientific, Singapore-New Jersey-Hong Kong, 1994.Google Scholar
[Po4] Popa, S.. Classification of subfactors and of their endomorphisms. CBMS Lecture Notes 1994. To appear.CrossRefGoogle Scholar
[PoS] Popa, S.. On a problem of R. V. Kadison on maximal Abelian *-subalgebras in factors. Invent. Math. 65 (1981), 269–281.CrossRefGoogle Scholar
[Po6] Popa, S.. An axiomatization of the lattice of higher relative commutants of a subfactor. ESI Preprint 115. July 1994.Google Scholar
[SV] Sunder, S. and Vijayavagan, A.. 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), 185–200.CrossRefGoogle Scholar