Pacific Journal of Mathematics

Duality for finite bipartite graphs (with an application to ${\rm II}_1$ factors).

Marie Choda

Article information

Pacific J. Math., Volume 158, Number 1 (1993), 49-65.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L37: Subfactors and their classification
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 46L35: Classifications of $C^*$-algebras


Choda, Marie. Duality for finite bipartite graphs (with an application to ${\rm II}_1$ factors). Pacific J. Math. 158 (1993), no. 1, 49--65.

Export citation


  • [1] J. Bion-Nadal, Subfactorof the hyperfinite Hi factor with Coxeter graph E as invariant, Current Topics in Operator algebras, World Scientific, (1991).
  • [2] O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc, 171 (1972), 195-234.
  • [3] F. M. Goodman, P. Harpe, and V. F. R. Jones, Coxeter Graphs and Towersof Algebras, Springer Verlag, 1989.
  • [4] U. Haagerup and K. Schou, Some new subfactors of the hyperfinite Hi-factor, preprint.
  • [5] M. Izumi, Application offusion rules to classificationof subfactors,to appear in Publ. RIMS.
  • [6] M. Izumi, Flatness of E%, Talk at the conference of Yamanakako (1991).
  • [7] V. F. R. Jones, Index for subfactors, Invent. Math., 72 (1983), 1-25.
  • [8] V. F. R. Jones, Braid groups,Hecke algebras and Type II1 factors, Geometric Methods in Operator Algebras, Pitman, Res. Notes in Math., 123 (1986), 242-273.
  • [9] Y. Kawahigashi,On flatness of Ocneanu's connections on the Dynkin diagrams and classificationof subfactors,preprint.
  • [10] Y. Kawahigashi, An analogue of a solvable lattice model in classification of subfactors, preprint.
  • [11] A. Ocneanu, Quantized groups,String Algebras and Galois Theoryfor Algebras, Operator Algebras and Applications, vol. II, London Math. Soc. Lecture Note Series, Cambridge Univ. Press, 136 (1988), 119-172.
  • [12] A. Ocneanu, Quantum symmetry, differential geometry of finite graphs and classifica- tion of subfactors,notes byKawahigashi.
  • [13] S. Okamoto, Invariantsfor subfactors arising from Coxeter graphs, preprint.
  • [14] S. Popa, Classificationof subfactors: the reductionto commuting squares,Invent. Math., 101 (1990), 19-43.
  • [15] S. Popa,Sur la classificationdes sousfacteurs d'indicefini dufacteur hyparfin, C.R. Acad. Sci. Paris, 311 (1990), 95-100.
  • [16] Ph. Roche, Ocneanu cell calculus and integrable lattice model, Comm. Math. Phys., 127 (1990), 395-424.
  • [17] K. Saito, Extended affine root systems I, Publ. RIMS, Kyoto Univ., 21 (1985), 75-179.
  • [18] S. Slodowy, Sur les GroupesFinis Attaches aux Singularites Simples, Introduc- tion a la Theorie des SingularitesII,Hermann, (1990), 109-125.
  • [19] M.Takesaki, Dualityfor crossedproducts andstructure of vonNeumann algebras of type III, Acta Math., 131 (1973), 249-310.
  • [20] H. Wenzl, Quantum groups and subfactors of type B, C, and D, Comm. Math. Phys., 133 (1990), 383-432.
  • [21] H. Wenzl,Heckealgebras of type An and subfactors,Invent. Math., 92 (1988), 349- 383.
  • [22] S. Popa, Relative dimension, towers of projections and commuting squares of subfactors, Pacific J. Math., 137 (1989), 181-207.