A Characterization of depth 2 subfactors of II1 factors

Journal of Functional Analysis

Volumn 171, Issue 2, 2000, Pages 278-307

  Nikshych, Dmitri ^a   Vainerman, Leonid ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034628705     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3522     Document Type: Article

References (27)

1. Bisch D. On the structure of finite depth subfactors. Algebraic Methods in Operator Theory. 1994;Birkhäuser. p. 175-194.
2. G. Böhm, F. Nill, and, K. Szlachányi, Weak Hopf algebras I: Integral theory and C*-structure, math.QA/9805116, 1998.
3. Böhm G., Szlachányi K. A coassociative C*-quantum group with nonintegral dimensions. Lett. in Math. Phys. 35:1996;473-476.
4. David M.-C. Paragroupe d'Adrian Ocneanu et algebre de Kac. Pacif. J. of Math. 172:1996;331-363.
5. Enock M., Nest R. Inclusions of factors, multiplicative unitaries and Kac algebras. J. Funct. Analysis. 137:1996;466-543.
6. Enock M., Vainerman L. Deformation of a Kac algebra by an abelian subgroup. Comm. Math. Phys. 178:1996;571-596.
7. Enock M., Vallin J.-M. Inclusions of von Neumann algebras and quantum groupoids. Inst. Math. de Jussieu. 1998.
8. Gantmacher F. R. Applications of the Theory of Matrices. 1959;Interscience Publishers.
9. Goodman F. M., de la Harpe P., Jones V. F. R. Coxeter Graphs and Towers of Algebras. MSRI Publ. 14. 1989;Springer-Verlag.
10. Jones V. Index for subfactors. Invent. Math. 72:1983;1-25.
11. Jones V., Sunder V. S. Introduction to Subfactors. 1997;Cambridge University Press.
12. Kac G. I. Certain arithmetic properties of ring groups. Functional Anal. Appl. 6:1972;158-160.
13. Longo R. A duality for Hopf algebras and subfactors I. Comm. Math. Phys. 159:1994;133-150.
14. Nikshych N., Vainerman L. Algebraic versions of a finite dimensional quantum groupoid Lecture Notes in Pure and Appl. Math. 1998.
15. 0-rings and twisting of finite dimensional semisimple Hopf algebras. Comm. in Algebra. 26:1998;321-342.
16. 1 factors, math.QA/9810049, 1998.
17. F. Nill, K. Szlachányi, and, H.-W. Wiesbrock, Weak Hopf algebras and reducible Jones inclusions of depth 2, I: From crossed products to Jones towers, math.QA/9806130, 1998.
18. F. Nill, Axioms for weak bialgebras, math.QA/9805104, 1998.
19. Pimsner M., Popa S. Entropy and index for subfactors. Ann. Sci. Ecole Norm. Sup. (4). 19:1986;57-106.
20. Pimsner M., Popa S. Iterating the basic construction. Trans. Amer. Math. Soc. 310:1988;127-133.
21. Popa S. Classification of amenable subfactors of type II. Acta Math. 172:1994;163-255.
22. Popa S. Classification of subfactors: the reduction to the commuting squares. Invent. Math. 101:1990;19-43.
23. Szymański W. Finite index subfactors and Hopf algebra crossed products. Proc. Amer. Math. Soc. 120:1994;519-528.
24. Vainerman L. 2-cocycles and twisting of Kac algebras. Comm. Math. Phys. 191:1998;697-721.
25. Vallin J.-M. Bimodules de Hopf et poids opératoriels de Haar. J. Operator Theory. 35:1996;39-65.
26. Watatani Y. Index for C*-subalgebras. Mem. Amer. Math. Soc. 424:1990.
27. Yamanouchi T. Duality for generalized Kac algebras and a characterization of finite groupoid algebras. J. Algebra. 163:1994;9-50.