Hostname: page-component-54dcc4c588-mz6gc Total loading time: 0 Render date: 2025-10-06T02:53:41.988Z Has data issue: false hasContentIssue false
  • English
  • Français

On Non-Strongly Free Automorphisms of Subfactors of Type $\text{II}{{\text{I}}_{0}}$

Published online by Cambridge University Press:  20 November 2018

Toshihiko Masuda
Toshihiko Masuda*
Affiliation:
Department of Mathematics Kochi University 2-5-1 Akebono-cho Kochi, 780-8520 Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We determine when an automorphism of a subfactor of type $\text{II}{{\text{I}}_{0}}$ with finite index is nonstrongly free in the sense of $\text{C}$ . Winsløw in terms of the modular endomorphisms introduced by M. Izumi.

Keywords

46L37

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 419 - 428
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Choda, M. and Kosaki, H., Strongly outer actions for an inclusion of factors. J. Funct. Anal. 122 (1994), 315–332.Google Scholar
[2] Connes, A. and Takesaki, M., The flow of weights on factors of type III. Tohoku J. Math. 29 (1977), 473–555.Google Scholar
[3] Evans, D. E. and Kawahigashi, Y., Quantum symmetries on operator algebras. Oxford Math. Monographs, Oxford University Press, 1998.Google Scholar
[4] Goodman, F. M., de la Harpe, P. and Jones, V. F. R., Coxeter graphs and towers of algebras. Springer-Verlag, 1989.Google Scholar
[5] Haagerup, U. and Størmer, E., Equivalence of normal states on von Neumann algebras and the flow of weights. Adv. Math. 83 (1990), 180–262.Google Scholar
[6] Haagerup, U. and Størmer, E., Pointwise inner automorphisms on von Neumann algebras. J. Funct. Anal. 92 (1990), 177–201.Google Scholar
[7] Hiai, F., Minimalizing indices of conditional expectations onto a subfactor. Publ. Res. Inst. Math. Soc. 24 (1988), 673–678.Google Scholar
[8] Isola, T., Modular structure of the crossed product by a compact group dual. J. Operator Theory 33 (1995), 3–32.Google Scholar
[9] Izumi, M., Application of fusion rules to classification of subfactors. Publ. Res. Inst.Math. Soc. 27 (1991), 953–994.Google Scholar
[10] Izumi, M., Canonical extension of endomorphisms on factors. In: Subfactors (eds. H. Araki et al.), World Scientific, 1994, 129–138.Google Scholar
[11] Izumi, M., Canonical extension of endomorphisms of type III factors. Amer. J. Math. 125 (2003), 1–56.Google Scholar
[12] Izumi, M. and Kawahigashi, Y., Classification of subfactors with principal graph Dn (1) J. Funct. Anal. 112 (1993), 257–286.Google Scholar
[13] Jones, V. F. R., Index for subfactors. Invent.Math. 72 (1983), 1–25.Google Scholar
[14] Katayama, Y., Sutherland, C. E. and Takesaki, M., The characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors. Invent.Math. 132 (1998), 331–380.Google Scholar
[15] Kawahigashi, Y. and Takesaki, M., Compact abelian group actions on injective factors. J. Funct. Anal. 105 (1992), 112–128.Google Scholar
[16] Kosaki, H., Extension of Jones’ theory on index to arbitrary factors. J. Funct. Anal. 66 (1986), 123–140.Google Scholar
[17] Kosaki, H., Automorphisms in the irreducible decomposition of sectors. In: Quantum and Non-commutative Analysis (eds. H. Araki et al.), Kluwer Academic Publishers, 1993, 305–316.Google Scholar
[18] Kosaki, H., AFD factor of type III0 with many isomorphic index 3 subfactors. J. Operator Theory 32 (1994), 17–29.Google Scholar
[19] Kosaki, H., Sector theory and automorphisms for factor-subfactor pairs. J. Math. Soc. Japan 48 (1996), 427–454.Google Scholar
[20] Kosaki, H. and Longo, R., A remark on the minimal index of subfactors. J. Funct. Anal. 107 (1992), 458–470.Google Scholar
[21] Kosaki, H. and Sano, T., Non-splitting inclusions of factors of type III0 . Pacific J. Math. 178 (1997), 95–125.Google Scholar
[22] Loi, P., On the derived towers of certain inclusions of type IIIλ factors of index 4. Pacific J. Math. 165 (1994), 321–345.Google Scholar
[23] Longo, R., Index of subfactors and statistics of quantum fields I. Comm. Math. Phys. 126 (1989), 217–247.Google Scholar
[24] Longo, R., Index of subfactors and statistics of quantum fields II. Comm. Math. Phys. 130 (1990), 285–309.Google Scholar
[25] Longo, R., Minimal index and braided subfactors. J. Funct. Anal. 109 (1992), 98–112.Google Scholar
[26] Pimsner, M. and Popa, S., Entropy and index for subfactors. Ann. Sci. École Norm. Sup. 19 (1986), 57–106.Google Scholar
[27] Popa, S., Classification actions of discrete amenable groups on subfactors of type II. Preprint, 1992.Google Scholar
[28] Sekine, Y., Flow of weights of the crossed products of type III factors by discrete groups. Publ. Res. Inst. Math. Sci. 26 (1990), 655–666.Google Scholar
[29] Winsløw, C., Strongly free actions on subfactors. Internat. J. Math. 4 (1993), 675–688.Google Scholar
[30] Winsløw, C., Classification of strongly amenable subfactors of type III0 . J. Funct. Anal 148 (1997), 296–313.Google Scholar
[31] Zimmer, R., Extensions of ergodic group actions. Illinois J. Math. 20 (1976), 373–409.Google Scholar